Finite groups in which every self-centralizing subgroup is a TI-subgroup or subnormal or has p′-order

Abstract

We first give complete characterizations of the structure of finite group [Formula: see text] in which every subgroup (or every non-nilpotent subgroup, or every non-abelian subgroup) is a TI-subgroup or subnormal or has [Formula: see text]-order for a fixed prime divisor [Formula: see text] of [Formula: see text]. Furthermore, we prove that every self-centralizing subgroup (or every self-centralizing non-nilpotent subgroup, or every self-centralizing non-abelian subgroup) of [Formula: see text] is a TI-subgroup or subnormal or has [Formula: see text]-order for a fixed prime divisor [Formula: see text] of [Formula: see text] if and only if every subgroup (or every non-nilpotent subgroup, or every non-abelian subgroup) of [Formula: see text] is a TI-subgroup or subnormal or has [Formula: see text]-order. Based on these results, we obtain the structure of finite group [Formula: see text] in which every self-centralizing subgroup (or every self-centralizing non-nilpotent subgroup, or every self-centralizing non-abelian subgroup) is a TI-subgroup or subnormal or has [Formula: see text]-order for a fixed prime divisor [Formula: see text] of [Formula: see text].