The Alternating Group A8 and the General Linerar Group GL4(2)

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Murray, John (1999) The Alternating Group A8 and the General Linerar Group GL4(2). Mathematical Proceedings of the Royal Irish Academy, 99A. pp. 123-132. ISSN 1393-7197

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Abstract

We give an explicit construction for the isomophism A8 GL4 (2). The involutions of cycle type 23 in the symmetric group S6, together with the null-set, can be given the structure of an elementary abelian group of order 16, in such a way that S6 preserves the group operation. This gives an embedding ( of S6 into the general linear group GL4(2). Regarding S6 as a subgroup of the alternating group A8, we show that ( extends to A8. Coincidence of group orders implues that this extension is an isomorphism.

Item Type:	Article
Keywords:	Alternating Group A8; General Linerar Group GL4(2);
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	2153
Depositing User:	Dr. John Murray
Date Deposited:	07 Oct 2010 11:19
Journal or Publication Title:	Mathematical Proceedings of the Royal Irish Academy
Publisher:	Royal Irish Academy
Refereed:	Yes
URI:	https://mural.maynoothuniversity.ie/id/eprint/2153
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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The Alternating Group A8 and the General Linerar Group GL4(2)

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