On the degree of groups of polynomial subgroup growth
نویسندگان
چکیده
منابع مشابه
On the Degree of Groups of Polynomial Subgroup Growth
Let G be a finitely generated residually finite group and let an(G) denote the number of index n subgroups of G. If an(G) ≤ nα for some α and for all n, then G is said to have polynomial subgroup growth (PSG, for short). The degree of G is then defined by deg(G) = limsup log an(G) log n . Very little seems to be known about the relation between deg(G) and the algebraic structure of G. We derive...
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15 صفحه اولON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1999
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-99-02220-5