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On the Jacobson radical of a block ideal in a finite p-solvable group for \(p\geq 5\). (English) Zbl 0507.16011


MSC:

16S34 Group rings
16Nxx Radicals and radical properties of associative rings
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20C05 Group rings of finite groups and their modules (group-theoretic aspects)

Citations:

Zbl 0096.251
Full Text: DOI

References:

[1] Dornhoff, L., Group Representation Theory, part B (1972), Marcel-Dekker: Marcel-Dekker New York · Zbl 0236.20004
[2] Feit, W., Representations of Finite Groups, parts I and II, (Lecture Notes (1975), Math. Dep., Yale Univ: Math. Dep., Yale Univ New Haven, Connecticut) · Zbl 0166.29002
[3] Fong, P., On the characters of \(p\)-solvable groups, Trans. Amer. Math. Soc., 98, 263-284 (1961) · Zbl 0096.25101
[4] Fong, P., Solvable groups and modular representation theory, Trans. Amer. Math. Soc., 103, 484-494 (1962) · Zbl 0105.25603
[5] Glauberman, G., A characteristic subgroup of a \(p\)-stable group, Canad. J. Math., 20, 1101-1135 (1968) · Zbl 0164.02202
[6] Glauberman, G., Global and local properties of finite groups, (Powell, M. B.; Higman, G., Finite Simple Groups (1971), Academic Press: Academic Press New York), 1-64 · Zbl 0167.29502
[7] Gorenstein, D., Finite Groups (1968), Harper & Row: Harper & Row New York · Zbl 0185.05701
[8] Huppert, B., Endliche Gruppen I (1967), Springer-Verlag: Springer-Verlag Berlin · Zbl 0217.07201
[9] Jennings, S. A., The structure of the group ring of a \(p\)-group over a modular field, Trans. Amer. Math. Soc., 50, 175-185 (1941) · Zbl 0025.24401
[10] Koshitani, S., On the nilpotency indices of the radicals of group algebras of \(p\)-solvable groups, (Proc. Japan Acad., 53A (1977)), 13-16 · Zbl 0388.16009
[11] Koshitani, S., On the nilpotency indices of the radicals of group algebras of \(p\)-groups which have cyclic subgroups of index \(p\), Tsukuba J. Math., 1, 137-148 (1977) · Zbl 0391.16007
[12] Michler, G. O., Blocks and centers of group algebras, (Lectures on Rings and Modules. Lectures on Rings and Modules, Lecture Notes in Math. No. 246 (1972), Springer-Verlag: Springer-Verlag Berlin), 429-563 · Zbl 0232.16011
[13] Morita, K., On group rings over a modular field which possess radicals expressible as principal ideals, Science Reports of Tokyo Bunrika Daigaku A4, 177-194 (1951) · Zbl 0053.35002
[14] Passman, D. S., Radicals of twisted group rings, (Proc. London Math. Soc., 20 (1970)), 409-437, (3) · Zbl 0192.35802
[15] Schwarz, W., Die Struktur modularer Gruppenringe endlicher Gruppen der \(p\)-Länge 1, J. Algebra, 60, 51-75 (1979) · Zbl 0418.20003
[16] Tsushima, Y., Radicals of group algebras, Osaka J. Math., 4, 179-182 (1967) · Zbl 0199.07601
[17] Tsushima, Y., Some notes on the radical of a finite group ring, Osaka J. Math., 15, 647-653 (1978) · Zbl 0394.16006
[18] Tsushima, Y., On the second reduction theorem of P. Fong, Kumamoto J. Science (Math.), 13, 6-14 (1978) · Zbl 0385.20004
[19] Wallace, D. A.R, Lower bounds for the radical of the group algebra of a finite \(p\)-soluble group, (Proc. Edinburgh Math. Soc., 16 (1968/1969)), 127-134 · Zbl 0167.02603
[20] Watanabe, A., On Fong’s reductions, Kumamoto J. Sci. (Math.), 13, 48-54 (1979) · Zbl 0406.20013
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