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A non-coprime Hall-Higman reduction theorem

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Yan-Ming Wang
Yan-Ming Wang
Affiliation:
Mathematics Department, Zhongshan University, Guangzhou 510275, People's Republic of China
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Abstract

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In a well-known paper, Hall and Higman proved the reduction theorem on a coprime order operator group acting on a finite group. This theorem plays an important role in local analysis of finite group theory. In this paper, we generalize the Hall-Higman reduction theorem by dropping the restrictive hypothesis (|G|, |H|) = 1 and determine the detailed structure of G completely.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Gorenstein, D., Finite simple groups (Plenum Press, New York, 1982).CrossRefGoogle Scholar
[2]Hall, P. and Higman, G., ‘The p-length of p-solvable groups and reduction theorems for Burnside's problem’, Proc. London Math. Soc. 6 (3) (1956), 1–14.CrossRefGoogle Scholar
[3]Huppert, B. and Blackburn, N., Finite groups III (Springer, New York, 1967).Google Scholar
[4]Kurzweil, H., Endliche Gruppen (Springer, New York, 1967).Google Scholar
[5]Schult, E., ‘Some analogues of Glauberman's Theorem’, Proc. Amer. Math. Soc. 17 (1966), 1186–1190.Google Scholar