University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > The generating graph of direct powers of simple groups

The generating graph of direct powers of simple groups

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For a finite group G, the generating graph Γ(G) is a graph whose vertices are the non-identity elements of G and two distinct vertices are connected by an edge if and only if they generate G. Many results on the generation of finite simple groups G can be equivalently stated as theorems on the generating graph of G: this assures to Γ(G) several good properties. In this talk, we will consider Γ(Gn), where G is a finite simple group and Gn a direct product of n copies of G: we will discuss whether the good generation properties of G affect the generating graph Γ(Gn) with particular attention to some questions on the diameter of Γ(Gn).

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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