Centrally large subgroup
From Groupprops
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 centrally large subgroup or CL-subgroup if it satisfies the following equivalent conditions:
- for any subgroup of .
- (i.e., is a self-centralizing subgroup of ) and is a centralizer-large subgroup of .
Equivalence of definitions
Further information: Centrally large iff centralizer-large and self-centralizing
Relation with other properties
Weaker properties
References
Journal references
- A measuring argument for finite groups by Andrew Chermak and Alberto Delgado, Proceedings of the American Mathematical Society, Volume 107,Number 4, Page 907 - 914(Year 1989): ^{Official copy}^{More info}
- 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}