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Finite groups with a self-centralizing subgroup of order 4

Published online by Cambridge University Press:  09 April 2009

Warren J. Wong
Warren J. Wong
Affiliation:
University of Notre DameNotre Dame, Indiana
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The class of finite groups having a subgroup of order 4 which is its own centralizer has been studied by Suzuki [9], Gorenstein and Walter [6], and the present author [11]. The main purpose of this paper is to strengthen Theorem 5 of [11] by using an early result of Zassenhaus [12]. In particular, we find all groups of the class which are core-free, i.e. which have no nontrivial normal subgroup of odd order. As an application, we make a determination of a certain class of primitive permutation groups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 570 - 576
Copyright
Copyright © Australian Mathematical Society 1967

References

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