On overgroups of a cycle rich in transvections. (Russian. English summary) Zbl 07845716
MSC:
20G15
Found 190 Documents (Results 1–100)
Comparison of Petrov’s odd elementary hyperbolic unitary group and Dickson-Siegel-Eichler-Roy elementary orthogonal group. (English) Zbl 1539.19005
Reviewer: Sourjya Banerjee (Kolkata)
Visualization for Petrov’s odd unitary group. (English) Zbl 1520.20105
Reviewer: Erich W. Ellers (Toronto)
Double coset Markov chains. (English) Zbl 1505.60068
\(p\)-groups and the polynomial ring of invariants question. (English) Zbl 1487.13014
Reviewer: Matyas Domokos (Budapest)
About subgroups rich in transvections. (Russian. English summary) Zbl 1513.20054
MSC:
20G35
Homomorphisms with condition (*) if 2 is a reversible element. (Ukrainian. English summary) Zbl 07909330
Images of formal matrices of elements of matrix groups over associative rings. (Ukrainian. English summary) Zbl 07909316
Properties of the commutators of some elements of linear groups over divisions rings. (English) Zbl 1464.15047
Residual and fixed modules. (English) Zbl 1464.16020
Fibred algebraic surfaces and commutators in the symplectic group. (English) Zbl 1470.14022
Reviewer: Ben Anthes (Marburg)
Invariants of polynomials mod Frobenius powers. (English) Zbl 1455.20027
Reviewer: Egle Bettio (Venezia)
Decomposition of elementary transvection in elementary net group. (Russian. English summary) Zbl 1488.20073
Simple closed curves, finite covers of surfaces, and power subgroups of \(\mathrm{Out}(F_n)\). (English) Zbl 1432.57041
Reviewer: Hongbin Sun (Piscataway)
An embedding theorem for an elementary net. (Russian. English summary) Zbl 1444.13012
Classification of subgroups of symplectic groups over finite fields containing a transvection. (English) Zbl 1341.20043
Automorphism groups of finite abelian \(p\)-groups and transvections. (English) Zbl 1346.20073
Reviewer: Marek Golasiński (Olsztyn)
On linear groups of degree 2 over a noncommutative division algebra. (English) Zbl 1346.20069
Reviewer: L. N. Vaserstein (University Park)
Equality of elementary linear and symplectic orbits with respect to an alternating form. (English) Zbl 1400.14126
On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings. (English) Zbl 1327.13032
Transvection modules in the overgroups of a non-split maximal torus. (Russian. English summary) Zbl 1333.20049
Corrigendum to “Free and non-free subgroups of the group \(\mathrm{UT}(\infty,\mathbb Z)\)”. (English) Zbl 1285.20050
On the extraction of transvections in overgroups of a non-split maximal torus. (Russian. English summary) Zbl 1326.20048
Stabilizers and orbits of first level vectors in modules for the special linear groups. (English) Zbl 1290.20032
Reviewer: Wilberd van der Kallen (Utrecht)
MSC:
20G05
Closed nets in linear groups. (English. Russian original) Zbl 1273.20047
Vestn. St. Petersbg. Univ., Math. 46, No. 1, 14-21 (2013); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2013, No. 1, 26-34 (2013).
Free and non-free subgroups of the group \(\mathrm{UT}(\infty,\mathbb Z)\). (English) Zbl 1275.20059
Commun. Algebra 41, No. 4, 1350-1364 (2013); corrigendum 42, No. 4, 1854 (2014).
Reviewer: L. N. Vaserstein (University Park)
Overgroups of \(E(m,R)\otimes E(n,R)\). I: Levels and normalizers. (English. Russian original) Zbl 1278.20069
St. Petersbg. Math. J. 23, No. 5, 819-849 (2012); translation from Algebra Anal. 23, No. 5, 55-98 (2011).
A generating set for the automorphism group of a graph product of Abelian groups. (English) Zbl 1242.20040
On subgroups normalized by \(\mathrm{EO}(2l,R)\). (English. Russian original) Zbl 1273.20046
Vestn. St. Petersbg. Univ., Math. 44, No. 4, 252-259 (2011); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2011, No. 4, 19-27 (2011).
Minimal decomposition of an automorphism. (Spanish. English summary) Zbl 1282.15007
MSC:
15A04
A ring determining the structure of overgroups of a non-split maximal torus. (Russian. English summary) Zbl 1232.20047
The group \(\text{Sp}_{10}(\mathbb Z)\) is \((2,3)\)-generated. (English) Zbl 1222.20022
Reviewer: Andrea Lucchini (Padova)
Two results for the automorphism group for partially commutative class two nilpotent groups. (Russian. English summary) Zbl 1249.20043
On subgroups of the general linear group that contain a nonsplit maximal torus. (English. Russian original) Zbl 1215.20044
J. Math. Sci., New York 171, No. 3, 380-385 (2010); translation from Zap. Nauchn. Semin. POMI 375, 130-139 (2010).
Parabolic subgroups of \(\mathrm{SL}_n\) and \(\mathrm{Sp}_{2l}\) over a Dedekind ring of arithmetic type. (English. Russian original) Zbl 1215.20047
J. Math. Sci., New York 171, No. 3, 307-316 (2010); translation from Zap. Nauchn. Semin. POMI 375, 5-21 (2010).
Transvections in subgroups of the general linear group containing a nonsplit maximal torus. (English. Russian original) Zbl 1202.20047
St. Petersbg. Math. J. 21, No. 5, 731-742 (2010); translation from Algebra Anal. 21, No. 5, 70-86 (2009).
Classification of the finite \(n\)-generator transvection groups over \(\mathbb Z_2\). (English) Zbl 1239.20068
Decomposition of transvections for automorphisms. (English. Russian original) Zbl 1211.20043
J. Math. Sci., New York 161, No. 4, 483-491 (2009); translation from Zap. Nauchn. Semin. POMI 365, 47-62 (2009).
Reviewer: Wilberd van der Kallen (Utrecht)
Subgroups of symplectic groups that contain a subsystem subgroup. (English. Russian original) Zbl 1312.20046
J. Math. Sci., New York 151, No. 3, 2937-2948 (2008); translation from Zap. Nauchn. Semin. POMI 349, 5-29 (2007).
Can one see the signs of structure constants? (English. Russian original) Zbl 1203.20041
St. Petersbg. Math. J. 19, No. 4, 519-543 (2008); translation from Algebra Anal. 19, No. 4, 34-68 (2007).
Yet another variation on the theme of decomposition of transvections. (English. Russian original) Zbl 1175.20043
Vestn. St. Petersbg. Univ., Math. 41, No. 4, 345-347 (2008); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2008, No. 4, 71-74 (2008).
On subnormal subgroups of linear groups. (Russian, English) Zbl 1154.20042
Sib. Mat. Zh. 49, No. 1, 218-223 (2008); translation in Sib. Math. J. 49, No. 1, 175-179 (2008).
Product of symplectic transvections for the element in the kernel\((\lambda)\). (Chinese. English summary) Zbl 1141.20306
On special congruence subgroups of symplectic groups. (English. Russian original) Zbl 1125.20036
Math. Notes 80, No. 5, 726-728 (2006); translation from Mat. Zametki 80, No. 5, 770-772 (2006).
The structure of subnormal subgroups of symplectic groups over local rings. (Russian, English) Zbl 1115.20037
Sib. Mat. Zh. 47, No. 3, 665-669 (2006); translation in Sib. Math. J. 47, No. 3, 551-554 (2006).
Subgroups of unitriangular groups of infinite matrices. (Russian, English) Zbl 1123.20039
Zap. Nauchn. Semin. POMI 338, 137-154 (2006); translation in J. Math. Sci., New York 145, No. 1, 4773-4780 (2007).
Polyvector representations of \(\text{GL}_n\). (Russian, English) Zbl 1125.20031
Zap. Nauchn. Semin. POMI 338, 69-97 (2006); translation in J. Math. Sci., New York 145, No. 1, 4737-4750 (2007).
The diameters of some classical groups with respect to a small generating set. (English) Zbl 1135.20033
Length problems for automorphisms of modules over local rings. (English) Zbl 1104.15016
Reviewer: Erich W. Ellers (Toronto)
Periodic simple groups of finitary linear transformations. (English) Zbl 1106.20038
Reviewer: B. A. F. Wehrfritz (London)
Decomposition of symplectic transformation for symplectic transvection over local rings. (Chinese. English summary) Zbl 1128.20309
Group generated by half transvections. (English) Zbl 1096.20032
Reviewer: L. N. Vaserstein (University Park)
Sets of transvections generating subgroups isomorphic to special linear groups. (English) Zbl 1084.20031
Reviewer: Erich W. Ellers (Toronto)
Orbits of groups generated by transvections over \(\mathbb{F}_2\). (English) Zbl 1088.20026
Reviewer: Erich W. Ellers (Toronto)
\(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces. (English) Zbl 1059.65040
Reviewer: Daniel Kressner (Zagreb)
Free products in linear groups. (English) Zbl 1044.20033
Reviewer: B. A. F. Wehrfritz (London)
Some completely reducible linear groups over a quaternion division ring containing a root subgroup. (English) Zbl 1049.20030
Reviewer: L. N. Vaserstein (University Park)
The number of connected components in double Bruhat cells for nonsimply-laced groups. (English) Zbl 1014.20016
Reviewer: Chen Chengdong (Shanghai)
Subnormal structure of two-dimensional linear groups over full rings. (English. Russian original) Zbl 1025.20036
Math. Notes 71, No. 6, 844-850 (2002); translation from Mat. Zametki 71, No. 6, 924-930 (2002).
Reviewer: L.N.Vaserstein (University Park)
Linear groups over a skew field of quaternions containing the group \(T_n(A,\Phi)\) over a subsfield. (English) Zbl 1016.20032
Reviewer: Li Fu-an (Beijing)
Products of commutators of transvections over local rings. (English) Zbl 1014.20022
Reviewer: Erich Ellers (Toronto)
A transvection decomposition in \(\text{GL}(n,2)\). (English) Zbl 1014.15002
Reviewer: Witold Wiȩsław (Wrocław)
Irreducible subgroups of symplectic groups in characteristic 2. (English) Zbl 1008.20043
Reviewer: U.Dempwolff (Kaiserslautern)
MSC:
20G40
On some extensions of \(\text{SU}(n,4)\). (Sur certaines extensions de \(\text{SU}(n,4)\).) (French) Zbl 1042.20021
The elements of the special linear group \(\text{SL}_nF\) as products of commutators of transvections. (English) Zbl 0989.20038
Reviewer: Erich Ellers (Toronto)
Fast recognition of classical groups over large fields. (English) Zbl 1012.20043
Kantor, William M. (ed.) et al., Groups and computation III. Proceedings of the international conference at the Ohio State University, Columbus, OH, USA, June 15-19, 1999. Berlin: Walter de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 8, 113-121 (2001).
Reviewer: Ye Jiachen (Shanghai)
Products of transvections in one conjugacy class of the symplectic group over the \(p\)-adic numbers. (English) Zbl 0985.15011
Reviewer: J.D.Dixon (Ottawa)
A third look at weight diagrams. (English) Zbl 1016.20029
Reviewer: Wilberd van der Kallen (Utrecht)
Simply laced Coxeter groups and groups generated by symplectic transvections. (English) Zbl 0998.20038
Reviewer: Chen Chengdong (Shanghai)
Connected components of real double Bruhat cells. (English) Zbl 0978.20021
Reviewer: Dan Laksov (Stockholm)
Structure of hyperbolic unitary groups. I: Elementary subgroups. (English) Zbl 0963.20024
Reviewer: Li Fu-an (Beijing)
Decomposition of transvections: A theme with variations. (English) Zbl 0944.20031
Reviewer: W.van der Kallen (Utrecht)
On the group of automorphisms of the free group. I: Transvections. (Sur le groupe d’automorphismes du groupe libre. I: Transvections.) (French) Zbl 0946.20018
Reviewer: S.Andreadakis (Athens)
Products of commutators of symplectic transvections. (Chinese) Zbl 0938.20036
Reviewer: Li Fuan (Beijing)
On the word length of commutators in \(\text{GL}_n(R)\). (English) Zbl 0935.20037
Reviewer: W.van der Kallen (Utrecht)
Groups generated by symplectic transvections over local rings. (English) Zbl 0984.20031
Reviewer: Huberta Lausch (Grafing)
Linear transvection groups and embedded polar spaces. (English) Zbl 0933.20036
Reviewer: E.Ellers (Toronto)
\(k\)-symplectic exterior systems. (Systèmes extérieurs \(k\)-symplectiques.) (French) Zbl 0946.53043
Linear transvection groups. (English) Zbl 0938.20037
Reviewer: E.Ellers (Toronto)
Subgroups isomorphic to \(G_2(L)\) in orthogonal groups. (English) Zbl 0914.20042
Reviewer: Li Fuan (Beijing)
Sur les groupes classiques. (On the classical groups). Nouveau tirage. (Sur les groupes classiques.) (French) Zbl 0926.20030
Paris: Hermann. 84 p. (1998).
Reviewer: A.-M.Aubert (Paris)
Subgroups of classical groups generated by transvections or Siegel transvections. II: Embeddings in orthogonal groups. (English) Zbl 0891.20035
Reviewer: Li Fuan (Beijing)
Subgroups of classical groups generated by transvections or Siegel transvections. I: Embeddings in linear groups. (English) Zbl 0891.20034
Reviewer: Li Fuan (Beijing)
Generation of certain matrix groups by three involutions, two of which commute. (English) Zbl 0886.20026
Reviewer: E.Ellers (Toronto)
A characterization of the symplectic and unitary \(3\)-transposition groups. (English) Zbl 0885.20021
Reviewer: G.Stroth (Halle)
Characterization of dilatations expressible as a product of independent simple transformations. (English) Zbl 0860.20038
Ershov, Y. (ed.) et al., Algebra. Proceedings of the third international conference on algebra, Krasnoyarsk, Russia, August 23-28, 1993. Berlin: Walter de Gruyter. 145-151 (1996).
Reviewer: Huberta Lausch (Deggendorf)
Subgroups of classical groups generated by transvections or Siegel transvections. (Untergruppen von klassischen Gruppen, die von Transvektionen oder Siegel-Transvektionen erzeugt werden.) (German) Zbl 0858.20031
Gießen: Univ. Gießen, FB Math. 187 p. (1995).
Non-commutative affine geometry and symbol calculus: Fourier transform magnetic resonance imaging and wavelets. (English) Zbl 0844.92011
On the decomposition of automorphisms of free modules into simple factors. (English. Russian original) Zbl 0896.20031
Izv. Math. 59, No. 2, 333-351 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 59, No. 2, 109-128 (1995).
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