A note on skeleton groups in coclass graphs

Heiko Dietrich, Subhrajyoti Saha

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Recent studies of p-groups of coclass r concentrate on the coclass graph (p,r). While the detailed structure of (p,r) is unknown, it is known that its general structure is dominated by the subgraph of 'skeleton groups'. The original definition of these groups is technical, but some modifications for special cases have been used successfully in the literature. Given their importance, in this paper we define and investigate skeleton groups more rigorously. In particular, we study their isomorphism problem, which is a crucial step towards understanding the skeleton subgraph of (p,r). During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on (3, 2). We correct these errors here by proving the required results in a more general context.

Original languageEnglish
Pages (from-to)127-146
Number of pages20
JournalInternational Journal of Algebra and Computation
Volume29
Issue number1
DOIs
Publication statusPublished - 1 Feb 2019

Keywords

  • coclass
  • p -Groups

Cite this

@article{fc8e2b77380e4abcbb6e38705f03e05f,
title = "A note on skeleton groups in coclass graphs",
abstract = "Recent studies of p-groups of coclass r concentrate on the coclass graph (p,r). While the detailed structure of (p,r) is unknown, it is known that its general structure is dominated by the subgraph of 'skeleton groups'. The original definition of these groups is technical, but some modifications for special cases have been used successfully in the literature. Given their importance, in this paper we define and investigate skeleton groups more rigorously. In particular, we study their isomorphism problem, which is a crucial step towards understanding the skeleton subgraph of (p,r). During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on (3, 2). We correct these errors here by proving the required results in a more general context.",
keywords = "coclass, p -Groups",
author = "Heiko Dietrich and Subhrajyoti Saha",
year = "2019",
month = "2",
day = "1",
doi = "10.1142/S0218196718500650",
language = "English",
volume = "29",
pages = "127--146",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing",
number = "1",

}

A note on skeleton groups in coclass graphs. / Dietrich, Heiko; Saha, Subhrajyoti.

In: International Journal of Algebra and Computation, Vol. 29, No. 1, 01.02.2019, p. 127-146.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A note on skeleton groups in coclass graphs

AU - Dietrich, Heiko

AU - Saha, Subhrajyoti

PY - 2019/2/1

Y1 - 2019/2/1

N2 - Recent studies of p-groups of coclass r concentrate on the coclass graph (p,r). While the detailed structure of (p,r) is unknown, it is known that its general structure is dominated by the subgraph of 'skeleton groups'. The original definition of these groups is technical, but some modifications for special cases have been used successfully in the literature. Given their importance, in this paper we define and investigate skeleton groups more rigorously. In particular, we study their isomorphism problem, which is a crucial step towards understanding the skeleton subgraph of (p,r). During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on (3, 2). We correct these errors here by proving the required results in a more general context.

AB - Recent studies of p-groups of coclass r concentrate on the coclass graph (p,r). While the detailed structure of (p,r) is unknown, it is known that its general structure is dominated by the subgraph of 'skeleton groups'. The original definition of these groups is technical, but some modifications for special cases have been used successfully in the literature. Given their importance, in this paper we define and investigate skeleton groups more rigorously. In particular, we study their isomorphism problem, which is a crucial step towards understanding the skeleton subgraph of (p,r). During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on (3, 2). We correct these errors here by proving the required results in a more general context.

KW - coclass

KW - p -Groups

UR - http://www.scopus.com/inward/record.url?scp=85062417105&partnerID=8YFLogxK

U2 - 10.1142/S0218196718500650

DO - 10.1142/S0218196718500650

M3 - Article

VL - 29

SP - 127

EP - 146

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 1

ER -