Proof of a Conjecture of Wiegold

2018/04/05 by Skutin, Alexander · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1804.01745

Abstract

In this short note we confirm a conjecture of James Wiegold. We prove that if G is a finite p-group and |G'|>p^n(n-1)/2 for some non-negative integer n, then the group G can be generated by the elements of breadth at least n. The breadth b(x) of an element x of a finite p-group G is defined by the equation |G:C_G(x)| = p^b(x), where C_G(x) is the centralizer of x in G.

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