Connected commuting graphs of finite groups can have arbitrarily large diameter

Details Connected commuting graphs of finite groups can have arbitrarily large diameter Connected commuting graphs of finite groups can have arbitrarily large diameter

2012-04-24

arxiv.org/abs/1204.5456v2

Mathematics

Group Theory

This article is being withdrawn after discovery an error in the proof of the main result which is potentially serious. It will

Scientific paper

We show that for every integer k >= 2, there exists a finite, non-abelian
group whose commuting graph is connected and has diameter k, thereby disproving
a conjecture of Iranmanesh and Jafarzadeh. We employ a probabilistic method,
and hence do not provide any explicit examples of finite groups whose commuting
graphs have large, finite diameter.

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