Covering Theorems in the Alternating Group
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Authors
Reineck, James F.
Issue Date
1978
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
It was shown by Ore [1951] that each element of A n, the alternating group on n letters, is a commutator, aba-lb-1 for some a and b in S n. Xu (1965] went further and showed that, given an element a in A n then, given any gEAn there is some b in A n such that g is conjugate to aba-lb-1. using the result of Xu it can be shown that there exist conjugacy classes C and C' in An such that CC' = A n. In this paper we will look at the
case where C = C' and determine whether some simple classes have the
property CC = A n. Section 2 looks at classes whose elements have period
two, utilizing results from Brenner, Randall and Riddell [1974].
Section three looks at classes whose elements have period three and
contains results of Brenner and Riddell [1976]. Section four looks at
coverings by classes whose elements all have period n (n odd) or
period n-1 (n even) and section five looks at the closely related
problem when, for n = 16k, the elements of the conjugacy classes all
have period n/4 using results from Brenner, Cranwell and Riddell [1973]
and [1974]. This paper then will summarize and complete details for
several different types of proofs.
Description
iii, 40 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.