A note on Oliver's p-group conjecture

作者：Xu, Xingzhong^*

来源：Journal of Algebra, 2018, 507: 421-427.

DOI：10.1016/j.jalgebra.2018.03.039

• Oliver's p-group
• The Thompson subgroup

Let S be a finite p-group for an odd prime p, Oliver proposed the conjecture that the Thompson subgroup J(S) is always contained in the Oliver subgroup x(S). That means he conjectured that vertical bar J(S)x(S) : x(S)vertical bar = 1. Let x(1)(S) be a subgroup of S such that x(1)(S)/x(S) is the center of S/x(S). In this short note, we prove that J(S) <= x(S) if and only if J(S) <= x(1)(S). As an easy application, we prove that vertical bar J(S)x(S) : x(S)vertical bar not equal P.

• 出版日期2018-8-1
• 单位湖北大学