Minimal CL-subgroup

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This article is about a maximality notion among subgroups, related to abelianness or small class, in a group of prime power order.
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Definition

Let $P$ be a group of prime power order. A subgroup $A$ of $P$ is termed a minimal CL-subgroup or minimal centrally large subgroup of $P$ if $A$ is a centrally large subgroup of $P$ and no proper subgroup of $A$ is a centrally large subgroup of $P$.

Relation with other properties

Weaker properties

• Centrally large subgroup

Facts

• All minimal CL-subgroups have the same commutator subgroup

References

Journal references

• Centrally large subgroups of finite p-groups by George Isaac Glauberman, Journal of Algebra, ISSN 00218693, Volume 300,Number 2, Page 480 - 508(Year 2006): ^{Official copyMore info}