The Mathieu group M₂₃ as additive functions on the finite field of size 2¹¹

2022/01/01 by Bing, Yiming, Hu, Bright, Hu, Ronni +8
#20C34 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2201.00108

Abstract

We explicitly extend the standard permutation action of the Mathieu group M₂₃ on a 23 element set C=C₂₃ contained in a finite field of 2¹¹ elements \mathbbF_2¹¹ to additive functions on this finite field. That is we represent M₂₃ as functions φ:\mathbbF_2¹¹→ \mathbbF_2¹¹ such that φ(x+y)=φ(x)+φ(y) and φ|_C is the standard permutation action. We give explicit 11× 11 matrices for the pair of standard generators of order 23 and order 5, as well as many tables to help facilitate future calculations.

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