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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]


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_ig^{-1} = B_i for all i \in I, there exists x \in N_G(H) such that xA_ix^{-1} = B_i for all i \in I.

Relation with other properties

Stronger properties

Weaker properties