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 language | English |
|---|---|
| Pages (from-to) | 127-146 |
| Number of pages | 20 |
| Journal | International Journal of Algebra and Computation |
| Volume | 29 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2019 |
Keywords
- coclass
- p -Groups
Cite this
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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 journal › Article › Research › peer-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 -