Actions of Alt(n) on groups of finite Morley rank without involutions

2022/05/12 by Altınel, Tuna, Wiscons, Joshua
#03C60 #20F11 (Primary) 20C30 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2205.06173

Abstract

We investigate faithful representations of Alt(n) as automorphisms of a connected group G of finite Morley rank. We target a lower bound of n on the rank of such a nonsolvable G, and our main result achieves this in the case when G is without involutions. In the course of our analysis, we also prove a corresponding bound for solvable G by leveraging recent results on the abelian case. We conclude with an application towards establishing natural limits to the degree of generic transitivity for permutation groups of finite Morley rank.

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