On Transiso Graph

2014/02/05 by Kakkar, Vipul, Mishra, Laxmi Kant
#05C25 #20N05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1402.1002

Abstract

In this note, we define a new graph Γ_d(G) on a finite group G, where d is a divisor of |G|. The vertices of Γ_d(G) are the subgroups of G of order d and two subgroups H₁ and H₂ of G are said to be adjacent if there exists S_i ∈ T(G,H_i) (i=1,2) such that S₁ ≅ S₂. We shall discuss the completeness of Γ_d(G) for various groups like finite abelian groups, dihedral groups and some finite p-groups.

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