Maximal abelian normal subgroups in Nilpotent groups of class 2
Group Theory
2016-07-05 v2
Abstract
A maximal abelian normal subgroup A in a nilpotent group N is self-centralizing. This makes their role an important one in determining the structure of the nilpotent group. For example if A is finite then N is also finite. In the free nilpotent group of class 2 such a group is always a cyclic extension of the center. However this need not be true in an arbitrary finitely generated class two nilpotent group. We show that three generator nilpotent groups violating this condition can be easily found. However in the case when there are four or more generators certain conditions must hold.
Cite
@article{arxiv.1606.09088,
title = {Maximal abelian normal subgroups in Nilpotent groups of class 2},
author = {Satvik Goswami and Ashish Gupta},
journal= {arXiv preprint arXiv:1606.09088},
year = {2016}
}