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Maximal Subgroups of Direct Products

✍ Scribed by Jacques Thévenaz

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
181 KB
Volume
198
Category
Article
ISSN
0021-8693

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✦ Synopsis

We determine all maximal subgroups of the direct product G n of n copies of a group G. If G is finite, we show that the number of maximal subgroups of G n is a quadratic function of n if G is perfect, but grows exponentially otherwise. We deduce a theorem of Wiegold about the growth behaviour of the number of generators of G n .

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