Involve: A Journal of Mathematics
- Volume 9, Number 5 (2016), 765-782.
On the Chermak–Delgado lattices of split metacyclic $p$-groups
The Chermak–Delgado measure of a subgroup of a finite group is defined as . The subgroups with maximal Chermak–Delgado measure form a poset and corresponding lattice, known as the CD-lattice of . We describe the symmetric nature of CD-lattices in general, and use information about centrally large subgroups to determine the CD-lattices of split metacyclic -groups in particular. We also describe a rank-symmetric sublattice of the CD-lattice of split metacyclic -groups.
Involve, Volume 9, Number 5 (2016), 765-782.
Received: 16 March 2015
Revised: 1 October 2015
Accepted: 27 October 2015
First available in Project Euclid: 22 November 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20D30: Series and lattices of subgroups
Brush, Erin; Dietz, Jill; Johnson-Tesch, Kendra; Power, Brianne. On the Chermak–Delgado lattices of split metacyclic $p$-groups. Involve 9 (2016), no. 5, 765--782. doi:10.2140/involve.2016.9.765. https://projecteuclid.org/euclid.involve/1511371068