Pronormality and Submaximal $\mathfrak {X}$$-Subgroups on Finite Groups

Abstract

According to Hall, a subgroup H of a group G is said to be pronormal if H and $H^g$$ are conjugate in $\langle H,H^g\rangle $$ for every $g\in G$$. In this survey, we discuss the role of pronormality for some subgroups of finite groups: Hall subgroups, subgroups of odd index, submaximal $\mathfrak X$$-subgroup, etc.

Keywords

Pronormal subgroup / $\pi $$-subgroup')">Hall $\pi $$-subgroup / $\mathfrak X$$-subgroup')">Submaximal $\mathfrak X$$-subgroup / Subgroup of odd index

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Funding

National Natural Science Foundation of China(11771409)