On the actions of finite permutation groups on groups of finite Morley rank

Tuna Altinel

Ever since the work of Borovik and Cherlin on permutation groups of finite Morley rank ([4]), there has been growing interest in faithful actions finite groups on various types of groups of finite Morley rank. This interest is due to various motivations: classifying highly generically transitive actions on sets ([1]), highly generically transitive representations, definable actions of finite groups on groups of finite Morley rank, automorphisms of groups of finite Morley rank. In my talk, I will give an overview of these lines of research and detail a recent result joint with Joshua Wiscons on lower bounds in the case of faithful actions of the alternating group on a nonsolvable group of finite Morley rank that does not contain involutions.

References

[1]

Tuna Altinel and Joshua Wiscons, Recognizing PGL₃ via generic 4-transitivity, Journal of the European Mathematical Society, vol. 20 (2018), no. 6, pp. 1525–1559.

[2]

Ayşe Berkman and Alexandre Borovik Groups of finite Morley rank with a generically sharply multiply transitive action, Journal of Algebra, vol. 368 (2012), no. X, pp. 237–250.

[3]

Ayşe Berkman and Alexandre Borovik Groups of finite Morley rank with a generically multiply transitive action on an abelian group, Arxiv, (2021), eprint 2107.09997.

[4]

Alexandre Borovik and Gregory Cherlin, Model theory with applications to algebra and analysis. Vol. 2, Model theory with applications to algebra and analysis. Vol. 2 (H. Dugald Macpherson, editors), Cambridge Univ. Press, Cambridge, 2008, pp. 30–50.

[5]

Luis Jaime Corredor and Adrien Deloro and Joshua Wiscons, Sym(n)- and Alt(n)-modules with an additive dimension, Arxiv, (2022), eprint 2111.11498.

This document was translated from L^AT_EX by H^EV^EA.

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