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A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups

Published online by Cambridge University Press:  20 November 2018

Martin R. Pettet
Martin R. Pettet*
Affiliation:
Texas A & M University, College Station, Texas
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Generalizing a celebrated theorem of Thompson, R. P. Martineau has established [4; 5] that a finite group which admits an elementary abelian group of automorphisms with trivial fixed-point subgroup is necessarily solvable. A critical observation in his approach to this problem is the fact that, corresponding to each prime divisor of its order, such a group contains a unique Sylow subgroup invariant (as a set) under the action. Hence, the theorem we shall derive here represents a modest extension of Martineau's result.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 848 - 855
Copyright
Copyright © Canadian Mathematical Society 1977

References

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