“School of Mathematics”Back to Papers Home
Back to Papers of School of Mathematics
|Paper IPM / M / 16716||
Given a finite group G with a normal subgroup N, the simple graph ΓG( N ) is a graph whose vertices are of the form |xG|, where x ∈ N\Z(G), and xG is the G-conjugacy class of N containing the element x. Two vertices |xG| and |yG| are adjacent if they are not co-prime. In this article we prove that, if ΓG(N) is a connected incomplete regular graph, then N = P ×A where P is a p-group, for some prime p, A ≤ Z(G), and Z(N)\not = N∩Z(G).
Download TeX format
|back to top|