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Creators/Authors contains: "Wiscons, Joshua"

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  1. ; (, Proceedings of the American Mathematical Society)
    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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  2. ; ; (, Journal of Algebra)
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  3. ; (, The Journal of Symbolic Logic)
    Abstract We show that any simple group of Morley rank 5 is a bad group all of whose proper definable connected subgroups are nilpotent of rank at most 2. The main result is then used to catalog the nonsoluble connected groups of Morley rank 5. 
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  4. ; (, Journal of the European Mathematical Society)
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  5. (, Bulletin of the London Mathematical Society)
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  6. (, The Journal of Symbolic Logic)
    Abstract We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2. 
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  7. (, Journal of Algebra)
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