Group in which every pronormal subgroup is normal

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A group in which every pronormal subgroup is normal is a group with the property that any pronormal subgroup of the group is a normal subgroup.

Relation with other properties

Stronger properties

• Nilpotent group
• Group in which every subgroup is subnormal
• Group satisfying normalizer condition
• Locally nilpotent group

Facts

For a finite group, every pronormal subgroup being normal is equivalent to the group being a finite nilpotent group.

References

• Transitivity of normality and pronormal subgroups by L. A. Kurdachenko and I. Ya. Subbotin, Combinatorial group theory, discrete groups, and number theory, Volume 421, Page 201 - 210(Year 2006): ^{More info}