Minimal CL-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 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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Contents
Definition
Let be a group of prime power order. A subgroup of is termed a minimal CL-subgroup or minimal centrally large subgroup of if is a centrally large subgroup of and no proper subgroup of is a centrally large subgroup of .
Relation with other properties
Weaker properties
Facts
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 copy}^{More info}