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Permutability of subgroups of G×H that are direct products of subgroups of the direct factors

✍ Scribed by J. Evan

Publisher
Springer
Year
2001
Tongue
English
Weight
93 KB
Volume
77
Category
Article
ISSN
0003-889X

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Maximal Subgroups of Direct Products
Maximal Subgroups of Direct Products
✍ Jacques Thévenaz 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 181 KB

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