A note on skeleton groups in coclass graphs

Author:

Dietrich Heiko1,Saha Subhrajyoti1

Affiliation:

1. School of Mathematical Sciences, Monash University, 1 Wellington Rd, 3800 Clayton, Australia

Abstract

Recent studies of [Formula: see text]-groups of coclass [Formula: see text] concentrate on the coclass graph [Formula: see text]. While the detailed structure of [Formula: see text] 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 [Formula: see text]. During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on [Formula: see text]. We correct these errors here by proving the required results in a more general context.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The origins of Coclass Theory;Archiv der Mathematik;2023-06-27

2. Orbit isomorphic skeleton groups;Algebra and Discrete Mathematics;2023

3. Galois trees in the graph of p-groups of maximal class;Journal of Algebra;2022-08

4. FINITEp-GROUPS AND COCLASS THEORY;Bulletin of the Australian Mathematical Society;2020-12-01

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