科研之友
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摘要
We construct, for d %26gt;= 2 and epsilon %26gt; 0, a d-generated p-group Gamma which, in an asymptotic sense, behaves almost like a d-generated free pro-p-group. We show that a subgroup of index p(n) needs (d - epsilon)p(n) generators, and that the subgroup growth of Gamma satisfies s(p)(n)(Gamma) %26gt; s(p)(n)(F-d(p))(1-epsilon), where F-d(p) is the d-generated free pro-p-group. To do this we introduce a new invariant for finitely-generated groups and study some of its basic properties.
- 出版日期2012-3
