Abstract.
Let G be a finitely generated pro-p group, and for every natural number n let s n (G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists αℝ≥0 such that s n (G)≤n α for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20].
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Mathematics Subject Classification (2000): 20E07.
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Klopsch, B. Pro-p groups with linear subgroup growth. Math. Z. 245, 335–370 (2003). https://doi.org/10.1007/s00209-003-0548-5
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DOI: https://doi.org/10.1007/s00209-003-0548-5