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A characterization of subgroup containment in direct products

✍ Scribed by Ben Brewster, Dandrielle Lewis

Book ID
118815385
Publisher
Springer Milan
Year
2012
Tongue
Italian
Weight
260 KB
Volume
61
Category
Article
ISSN
0035-5038

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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