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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

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