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A Note on Partition-Inducing Automorphism Groups

Published online by Cambridge University Press:  20 November 2018

Martin R. Pettet
Martin R. Pettet*
Affiliation:
University of ToledoToledo, Ohio 43606, U.S.A.
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Abstract

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We consider a finite group G with a group A acting on it in such a way as to induce a partition of G# (a situation which arises in the study of centralizer near-rings). With the additional hypothesis that (|Aω|, |G|) = 1, it is shown that either A is semiregular on G# or G is an irreducible module for A.

Keywords

20D9916A76
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 157 - 159
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Glauberman, G., Fixed points in groups with operator groups, Math. Zeitschrift 84 (1964), 120–125.Google Scholar
2. Gorenstein, D., Finite Groups (Harper and Row, New York, 1968).Google Scholar
3. Isaacs, I. M. and Passman, D. S., Half-transitive automorphism groups, Can. J. Math. 18 (1966), 1243–1250.Google Scholar
4. Maxson, C. and Smith, K., The centralizer of a set of group automorphisms, Comm. in Algebra 8 (1980), 211–229.Google Scholar
5. Pettet, M., Nilpotent partition-inducing automorphism groups, Can. J. Math. 33 (1981), 412–420.Google Scholar