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Monomial Modular Representations and Construction of the Held Group

✍ Scribed by R.T. Curtis

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 230 KB
Volume: 184
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0307

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✦ Synopsis

Monomial representations of familiar finite groups over finite fields are used to Ž . construct infinite semi-direct products of free products of cyclic groups by groups of monomial automorphisms. Finite homomorphic images of these progenitors in which the actions on the group of automorphisms and on the cyclic components are faithful are sought. The smallest non-trivial images of this type are often sporadic simple groups. The technique is demonstrated by three examples over the fields Z , Z , and Z , which produce the Mathieu group M , the unitary group 3 5 7 1 1

Ž . U 5 : 2, and the Held group, respectively.

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