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The Subgroups of Direct Products of Surface Groups

✍ Scribed by Martin R. Bridson; James Howie; Charles F. Miller; Hamish Short


Book ID
110389648
Publisher
Springer
Year
2002
Tongue
English
Weight
118 KB
Volume
92
Category
Article
ISSN
0046-5755

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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