Self-conjugate-permutable subgroup

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History

Origin

The notion of self-conjugate-permutable subgroup was introduced by Shirong Li and Zhongchuan Meng, in their paper Groups with Conjugate-permutable conditions.

Definition

Symbol-free definition

A subgroup of a group is termed self-conjugate-permutable if the only conjugate subgroup with which it permutes, is itself.

Definition with symbols

A subgroup H of a group G is termed self-conjugate-permutable if whenever g \in G is such that HH^g = H^gH, then H^g = H. Here H^g = gHg^{-1}.

Relation with other properties

Stronger properties

Opposite properties

References

  • Groups with conjugate-permutable conditions by Shirong Li and Zhongchuan Meng, Mathematical Proceedings of the Royal Irish Academy