A restriction on centralizers in finite groups

作者：Fernandez Alcober Gustavo A^*; Legarreta Leire; Tortora Antonio; Tota Maria

来源：Journal of Algebra, 2014, 400: 33-42.

DOI：10.1016/j.jalgebra.2013.10.032

• Centralizers
• Finite groups

For a given m %26gt;= 1, we consider the finite non-abelian groups G for which vertical bar C-G(g) : %26lt; g %26gt;vertical bar %26lt;= m for every g epsilon G \ Z(G). We show that the order of G can be bounded in terms of m and the largest prime divisor of the order of G. Our approach relies on dealing first with the case where G is a non-abelian finite p-group. In that situation, if we take m = p(k) to be a power of p, we show that vertical bar G vertical bar %26lt;= p(2k+2) with the only exception of Q(8). This bound is best possible, and implies that the order of G can be bounded by a function of m alone in the case of nilpotent groups.

• 出版日期2014-2-15