Some Groups with Computable Chermak-Delgado Lattices
Group Theory
2014-07-24 v1
Abstract
Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the collection of all subgroups of G with maximal Chermak-Delgado measure, denoted CD(G), is a sublattice of the lattice of all subgroups of G. In this paper we note that the members of CD(G) are subnormal in G and determine the Chermak-Delgado lattice of direct products. We additionally describe the lattice for certain kinds of wreath products and examine the behavior of centrally large subgroups, a subset of the Chermak-Delgado lattice.
Keywords
Cite
@article{arxiv.1202.2385,
title = {Some Groups with Computable Chermak-Delgado Lattices},
author = {Ben Brewster and Elizabeth Wilcox},
journal= {arXiv preprint arXiv:1202.2385},
year = {2014}
}