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