Remarks on a class of 2-generator groups of deficiency zero

nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2

Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.

On the Structure of Some Deficiency Zero Groups

Generator 2 - Groups of Class Two

A group is called capable if it is a central factor group. We characterize the capable 2-generator 2-groups of class 2 in terms of a standard presentation.

nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2

here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. also we find integers $n$ for which, these groups are $n$-central.

Groups of deficiency zero

We make a systematic study of groups of deeciency zero, concentrating on groups of prime-power order. We prove that a number of p-groups have deeciency zero and give explicit balanced presentations for them. This signiicantly increases the number of such groups known. We describe a reasonably general computational approach which leads to these results. We also list some other nite groups of dee...