ON THE DIAMETER OF A GRAPH RELATED TO CONJUGACY CLASSES OF GROUPS

Citation
D. Chillag et al., ON THE DIAMETER OF A GRAPH RELATED TO CONJUGACY CLASSES OF GROUPS, Bulletin of the London Mathematical Society, 25, 1993, pp. 255-262
Citations number
5
Categorie Soggetti
Mathematics, General",Mathematics
ISSN journal
00246093
Volume
25
Year of publication
1993
Part
3
Pages
255 - 262
Database
ISI
SICI code
0024-6093(1993)25:<255:OTDOAG>2.0.ZU;2-T
Abstract
Let G be a finite group. Attach to G the following graph F: its vertic es are the non-central conjugacy classes of G, and two vertices are co nnected if their cardinalities are not co-prime. Denote by n(GAMMA) th e number of the connected components of GAMMA. By [1], n(GAMMA) less-t han-or-equal-to 2 for all finite groups, and if GAMMA is connected. th e diameter of the graph is at most 4. In this paper we prove that if G AMMA is connected, then the diameter of the graph is at most 3, and th is bound is the best possible. Similar results are proved for infinite FC-groups.