Abstract
The study of subgroup growth in finitely generated groups begins with the observation that there are only finitely many subgroups of each finite index. By considering homomorphisms of a d-generator group G into Sym(n), we showed in §1.1 that an(G) ≤ n · (n!)d-1 for each n. It is not much harder to see that asymptotically this bound is achieved. Rather surprisingly, the same applies also to the number mn(G) of maximal subgroups of index n. The precise result is Theorem 2.1 Let F be a free group on d ≥ 2 generators. Then a n (F)~m n (F)~n · (n!)d-1 .
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© 2003 Birkhäuser Verlag
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Lubotzky, A., Segal, D. (2003). Free Groups. In: Subgroup Growth. Progress in Mathematics, vol 212. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8965-0_3
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DOI: https://doi.org/10.1007/978-3-0348-8965-0_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9846-1
Online ISBN: 978-3-0348-8965-0
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