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Groups whose prime graph on class sizes has a cut vertex
- Source :
- Israel Journal of Mathematics. 244:775-805
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Let $G$ be a finite group, and let $\Delta(G)$ be the prime graph built on the set of conjugacy class sizes of $G$: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, two vertices $p$ and $q$ being adjacent if and only if $pq$ divides some conjugacy class size of $G$. In the present paper, we classify the finite groups $G$ for which $\Delta(G)$ has a cut vertex.
- Subjects :
- Class (set theory)
Finite group
General Mathematics
Prime number
Group Theory (math.GR)
Vertex (geometry)
Set (abstract data type)
Combinatorics
Conjugacy class
Simple (abstract algebra)
Prime graph
FOS: Mathematics
20E45
Finite groups, Conjugacy classes, Prime graph
Mathematics - Group Theory
Mathematics
Subjects
Details
- ISSN :
- 15658511 and 00212172
- Volume :
- 244
- Database :
- OpenAIRE
- Journal :
- Israel Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....cabaccea6899bfda701784e156820667