• Corpus ID: 244488162

Sym(n)- and Alt(n)-modules with an additive dimension

  title={Sym(n)- and Alt(n)-modules with an additive dimension},
  author={Luis Jaime Corredor and Adrien Deloro and Joshua Wiscons},
We revisit, clarify, and generalise classical results of Dickson and (much later) Wagner on minimal Sym(n)and Alt(n)-modules. We present a new, natural notion of ‘modules with an additive dimension’ covering at once the classical, finitary case as well as modules definable in an o-minimal or finite Morley rank setting; in this context, we fully identify the faithful Sym(n)and Alt(n)-modules of least dimension. § 
1 Citations
Actions of $\operatorname{Alt}(n)$ on groups of finite Morley rank without involutions
. 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


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We investigate the configuration where a group of finite Morley rank acts definably and generically m-transitively on an elementary abelian p-group of Morley rank n, where p is an odd prime, and m >
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  • Mathematics
    The Journal of Symbolic Logic
  • 2020
This work deduces chain conditions for groups, definability results for fields and domains, and shows that a pseudofinite group of dimension 1 contains a soluble subgroup of dimension 2.
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For each integer m , Rasala [6] has shown how to list all the ordinary irreducible representations of the symmetric group n which have degree less than n m , provided that n is large enough, and in
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We present here a new approach to the description of finite-dimensional complex irreducible representations of the symmetric groups due to A. Okounkov and A. Vershik. It gives an alternative
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An identification theorem for the natural module of SL2 in the finite Morley rank category is proved and it is shown that there are essentially two natural actions of SL( V) and GL(V) with V a vector space of dimension 2.
Model theory with applications to algebra and analysis
Preface List of contributors 1. Conjugacy in groups of finite Morley rank Olivier Frecon and Eric Jaligot 2. Permutation groups of finite Morley rank Alexandre Borovik and Gregory Cherlin 3. A survey
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1. In a series of articles in the Berliner Berichte, beginning in 1896, Frobenius has developed an elaborate theory of group-characters and applied it to the representation of a given finite group
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