MWNSCDIN-subgroup

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Definition

Symbol-free definition

A subgroup of a group is termed a MWNSCDIN-subgroup if it is a multiple weak normal subset-conjugacy-determined subgroup inside its normalizer relative to the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed a MWNSCDIN-subgroup if, given a collection of normal subsets $A_{i},i\in I$ and $B_{i},i\in I$ of $H$ , and an element $g\in G$ such that $gA_{i}g^{-1}=B_{i}$ for all $i\in I$ , there exists $x\in N_{G}(H)$ such that $xA_{i}x^{-1}=B_{i}$ for all $i\in I$ .