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Covering Theorems for FINASIGS VIII—almost all conjugacy classes in An have exponent ≤4

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

J. L. Brenner
J. L. Brenner
Affiliation:
10 Phillips Road Palo Alto, CA 94303
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Abstract

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The product of two subsets C, D of a group is defined as . The power Ce is defined inductively by C0 = {1}, Ce = CCe−1 = Ce−1C. It is known that in the alternating group An, n > 4, there is a conjugacy class C such that CC covers An. On the other hand, there is a conjugacy class D such that not only DD≠An, but even De≠An for e<[n/2]. It may be conjectured that as n ← ∞, almost all classes C satisfy C3 = An. In this article, it is shown that as n ← ∞, almost all classes C satisfy C4 = An.

MSC classification

Secondary: 20D05: Finite simple groups and their classification
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 210 - 214
Copyright
Copyright © Australian Mathematical Society 1978

References

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