Original Articles

On the ranks of Fi₂₂

Published in: Quaestiones Mathematicae
Volume 37 , issue 4 , 2014 , pages: 591–600

DOI: 10.2989/16073606.2014.894692

Author(s): Faryad Ali Department of Mathematics, Saudi Arabia

Keywords: Fischer group Fi₂₂ , rank , generator , sporadic group , Fischer group Fi₂₂ , rank , generator , sporadic group

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Abstract

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G:X) to be the minimum number of elements of X generating G. Moori investigated rank(Fi₂₂:X), where X is a conjugacy class of involutions in the Fischer group Fi₂₂. In the present article, we completely determine the ranks of the Fischer group Fi₂₂ by computing rank(Fi₂₂:X), where X is any conjugacy class of Fi₂₂.

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