1. A note on skeleton groups in coclass graphs
- Author
-
Heiko Dietrich and Subhrajyoti Saha
- Subjects
Combinatorics ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,Graph ,Mathematics - 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.
- Published
- 2019