James Williams

activity

20182021

p

-groups

1 citations · 1 across the 3 of their papers we have counts for

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math.GR2021

On finite $p$ -groups with powerful subgroups

James Williams

In this paper we investigate the structure of finite $p$ -groups with the property that every subgroup of index $p^{i}$ is powerful for some $i$ . For odd primes $p$ , we show that unde…

math.GR2020

On the regular power structure of $p$ -groups and applications

James Williams

In this paper, we give elementary proofs of the Restricted Burnside Problem and the Hughes Conjecture for finite $p$ -groups with Hall's regular power structure property. Moreover,…

math.GR2020

Powerfully nilpotent groups of rank 2 or small order

Gunnar Traustason, James Williams

In this paper we continue the study of powerfully nilpotent groups. These are powerful $p$ -groups possessing a central series of a special kind. To each such group one can attach a…

math.GR2019★ 1 cited

Quasi-powerful $p$ -groups

James Williams

In this paper we introduce the notion of a quasi-powerful $p$ -group for odd primes $p$ . These are the finite $p$ -groups $G$ such that $G / Z (G)$ is powerful in the sense of Lubotzky…

math.GR2019

Normal Subgroups of Powerful $p$ -groups

James Williams

In this note we show that if $p$ is an odd prime and $G$ is a powerful $p$ -group with $N \leq G^{p}$ and $N$ normal in $G$ , then $N$ is powerfully nilpotent. An analogous result is…

math.GR2018

Powerfully nilpotent groups

Gunnar Traustason, James Williams

We introduce a special class of powerful $p$ -groups that we call powerfully nilpotent groups that are finite $p$ -groups that possess a central series of a special kind. To these we…

On finite p-groups with powerful subgroups

On the regular power structure of p-groups and applications

Powerfully nilpotent groups of rank 2 or small order

Quasi-powerful p-groups

Normal Subgroups of Powerful p -groups

Powerfully nilpotent groups

On finite $p$ -groups with powerful subgroups

On the regular power structure of $p$ -groups and applications

Quasi-powerful $p$ -groups

Normal Subgroups of Powerful $p$ -groups