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The Number of Generators of Finite Linear Groups

✍ Scribed by Fisher, R. K.

Book ID
120094571
Publisher
Oxford University Press
Year
1974
Tongue
English
Weight
67 KB
Volume
6
Category
Article
ISSN
0024-6093

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πŸ“œ SIMILAR VOLUMES

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In 1991 Dixon and Kovacs 8 showed that for each field K which has finite degree over its prime subfield there is a number d such that every K finite nilpotent irreducible linear group of degree n G 2 over K can be w x wx ' generated by d nr log n elements. Afterwards Bryant et al. 3 proved K ' d G F

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We study the number of homomorphisms from a finite group to a general linear group over a finite field. In particular, we give a generating function of such numbers. Then the Rogers-Ramanujan identities are applicable.

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We prove that the analog of the Grushko-Neumann theorem does not hold for profinite free products of profinite groups. To do that we bound the number of generators of a finite group generated by a family of subgroups of pairwise coprime orders.