Groups Whose Chermak-Delgado Lattice is a Chain
Group Theory
2014-07-24 v1
Abstract
For a finite group G with subgroup H the Chermak-Delgado measure of H in G refer to the product of the order of H with the order of its centralizer, C_G(H). The set of all subgroups with maximal Chermak-Delgado measure form a sublattice, CD(G), within the subgroup lattice of G. This paper examines conditions under which the Chermak-Delgado lattice is a chain of subgroups. On the basis of a general result how to extend certain Chermak-Delgado lattices, we construct for any prime p and any non-negative integer n a p-group whose Chermak-Delgado lattice is a chain of length n.
Keywords
Cite
@article{arxiv.1305.2327,
title = {Groups Whose Chermak-Delgado Lattice is a Chain},
author = {Ben Brewster and Peter Hauck and Elizabeth Wilcox},
journal= {arXiv preprint arXiv:1305.2327},
year = {2014}
}