Document Zbl 0526.20038

Sylow-p-subgroups of p-solvable subgroups of GL(n,p). (English) Zbl 0526.20038

Arch. Math. 43, 1-10 (1984).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0526.20038

MSC:

20G40	Linear algebraic groups over finite fields
20D20	Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure

Keywords:

p-solvable completely reducible group; order of Sylow-p-subgroup; p- length; p-rank

Citations:

Zbl 0232.20008; Zbl 0153.040; Zbl 0079.037; Zbl 0073.255

Cite Review PDF

Full Text: DOI

References:

[1]	W. Burnside, On group of orderp a q b II. Proc. London Math. Soc.2, 432-437 (1904). · JFM 36.0198.02 · doi:10.1112/plms/s2-2.1.432
[2]	J. Dixon, Normalp-subgroups of solvable linear groups. J. Australian Math. Soc.7, 545-551 (1967). · Zbl 0153.04002 · doi:10.1017/S1446788700004481
[3]	L.Dornhoff, Group Representation Theory. New York 1972. · Zbl 0236.20004
[4]	W. Feit andJ. Thompson, Solvability of groups of odd order. Pacific J. Math.13, 755-1029 (1963). · Zbl 0124.26402
[5]	D.Gorenstein, Finite Groups. New York 1968.
[6]	P. Hall andG. Higman, On thep-length ofp-solvable groups and reduction theorems for Burnside’s problem. Proc. London Math. Soc.6, 1-40 (1956). · Zbl 0073.25503 · doi:10.1112/plms/s3-6.1.1
[7]	B. Huppert, Lineare aufl?sbare Gruppen. Math. Z.67, 479-518 (1957). · Zbl 0079.03701 · doi:10.1007/BF01258878
[8]	B.Huppert, Endliche Gruppen I. Berlin 1967. · Zbl 0217.07201
[9]	B.Huppert and N.Blackburn, Finite Groups II. Berlin 1982. · Zbl 0477.20001
[10]	I. M. Isaacs, Characters of solvable and symplectic groups. Amer. J. Math.95, 594-635 (1973). · Zbl 0277.20008 · doi:10.2307/2373731
[11]	I. M.Isaacs, Character Theory of Finite Groups. New York 1976. · Zbl 0337.20005
[12]	R.Maier and S.Sidki, A note of subnormality in factorizable finite groups. Arch. Math. (to appear). · Zbl 0544.20020
[13]	D. L. Winter,p-solvable linear groups of finite order. Trans. Amer. Math. Soc.157, 155-160 (1971). · Zbl 0232.20008
[14]	T. R. Wolf, Solvable and nilpotent subgroups ofGL (n, q m). Canadian J. Math.34, 1097-1111 (1982). · doi:10.4153/CJM-1982-079-5

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.