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Structure of р-Solvable Groups With Three р-Regular Classes

Published online by Cambridge University Press:  20 November 2018

Yasushi Ninomiya
Yasushi Ninomiya*
Affiliation:
Department of Mathematics Faculty of Liberal Arts Shinshu University Matsumoto, 390 Japan
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One of the important invariants of a р-block B of a group algebra is ℓ (B), the number of non-isomorphic simple B-modules. A number of authors calculated ℓ (B) for various types of defect groups of B. In particular, by Olsson [6], it has been proved that if p = 2 and the defect groups of the block B are dihedral or semi-dihedral or generalized quaternion, then ℓ (B) is at most 3. In this paper, we restrict our attention to the principal p-block B0 of a finite р-solvable group with ℓ (B0) ≤ 3. Let Γ be a finite р-solvable group and k a splitting field for Γ with characteristic р.

Keywords

20C2020D99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 559 - 579
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Gorenstein, D., Finite groups. Harper & Row, New York, 1968.Google Scholar
2. Huppert, B. and Blackburn, N., Finite groupsII, III. Springer-Verlag, Berlin, 1982.Google Scholar
3. Isaacs, I.M. and Passman, D.S., Half-transitive automorphism groups, Canad. J. Math. 18(1966), 1243–1250.Google Scholar
4. Koshitani, S., On group algebras of finite groups, in Représentation Theory II, Groups and Orders (Proc. 4th Int. Conf., Ottawa/Can. 1984), Lecture Notes Math. 1178 Springer-Verlag, Berlin, 1986, 109–128.Google Scholar
5. Ninomiya, Y. and Wada, T., Cartan matrices for blocks of finite p-solvable groups with two simple modules, to appear in J. Algebra.Google Scholar
6. Olsson, J.B., On 2-blocks with quaternion and quasidihedral defect groups, J. Algebra 36(1975), 212–241.Google Scholar
7. Passman, D.S., Permutation groups. Benjamin, New York, 1968.Google Scholar