Powering-invariance is not commutator-closed
This article gives the statement, and possibly proof, of a subgroup property (i.e., powering-invariant subgroup) not satisfying a subgroup metaproperty (i.e., commutator-closed subgroup property).
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- Powering-invariance is commutator-closed in nilpotent group
- Powering-invariance is not finite-join-closed
- Powering-invariance is strongly join-closed in nilpotent group
Suppose is the generalized dihedral group corresponding to the additive group of rational numbers. Let and both be subgroups of order two generated by different reflections. Then, the following are true: