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Koshitani, Shigeo

On the nilpotency indices of the radicals of group algebras of p-solvable groups. (English) Zbl 0388.16009

Proc. Japan Acad., Ser. A 53, 13-16 (1977).
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Cited in 2 Documents

MSC:

16S34 Group rings
16Nxx Radicals and radical properties of associative rings
16D40 Free, projective, and flat modules and ideals in associative algebras
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
20C20 Modular representations and characters
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References:

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[2] D. Gorenstein: Finite Groups. Harper and Row, New York (1968). · Zbl 0185.05701
[3] P. Hall and G. Higman: On the p-length of p-soluble groups and reduction theorems for Burnside’s problem. Proc. London Math. Soc, 6, 1-42 (1956). · Zbl 0073.25503 · doi:10.1112/plms/s3-6.1.1
[4] H. Kupisch: Projektive Moduln endlicher Gruppen mit zyklischer p-SylowGruppe. J. Alg., 10, 1-7 (1968). · Zbl 0164.02701 · doi:10.1016/0021-8693(68)90101-4
[5] H. Kupisch: Symmetrische Algebren mit endlich vielen unzerlegbaren Darstellungen II. J. Reine Angew. Math., 245, 1-14 (1970). · Zbl 0228.16010 · doi:10.1515/crll.1970.245.1
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[7] K. Morita: On group rings over a modular field which possess radicals expressible as principal ideals. Sci. Rep. of Tokyo Bunrika Daigaku, A4, 177-194 (1951). · Zbl 0053.35002
[8] K. Motose and Y. Ninomiya: On the nilpotency index of the radical of a group algebra. Hokkaido Math. J., 2, 261-264 (1975). · Zbl 0314.16012
[9] D. S. Passman: Radicals of twisted group rings. Proc. London Math. Soc, 20, 409-437 (1970). · Zbl 0192.35802 · doi:10.1112/plms/s3-20.3.409
[10] B. Srinivasan: On the indecomposable representations of a certain class of groups. Proc. London Math. Soc, 10, 497-513 (1960). · Zbl 0100.25705 · doi:10.1112/plms/s3-10.1.497
[11] Y. Tsushima: Radicals of group algebras. Osaka J. Math., 4, 179-182 (1967). · Zbl 0199.07601
[12] D. A. R. Wallace: Lower bounds for the radical of the group algebra of a finite p-soluble group. Proc. Edinburgh Math. Soc, 16, 127-134 (1968). · Zbl 0167.02603 · doi:10.1017/S0013091500012505
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