3-transpositions in infinite groups
- 1 November 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 96 (3) , 371-377
- https://doi.org/10.1017/s0305004100062290
Abstract
Let G be a group. A subset D will be called a set of 3-transpositions if |x| = 2 for xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx−1 = D for each xεD. For each xεD, let For each subset X of D, we denote by [X] the graph with vertex set X where two elements x, yεX are joined by an edge whenever they commute. We denote by (X) the complement graph; thus two elements x, yεX are joined by an edge of (X) whenever they do not commute.This publication has 4 references indexed in Scilit:
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