Semipermutable subgroup

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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]
This is a variation of permutability|Find other variations of permutability |

Definition

Symbol-free definition

A subgroup of a finite group is termed semipermutable if it permutes with every subgroup whose order is relatively prime to it.

Definition with symbols

A subgroup H of a finite group G is termed semipermutable if for any group K such that the orders of H and K are relatively prime, HK = KH.

Relation with other properties

Stronger properties