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Isogeny in superstable groups

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Abstract

We study and develop a notion of isogeny for superstable groups inspired by the notion in algebraic groups and differential algebraic notions developed by Cassidy and Singer. We prove several fundamental properties of the notion. Then we use it to formulate and prove a uniqueness results for a decomposition theorem about superstable groups similar to one proved by Baudisch. Connections to existing model theoretic notions and existing differential algebraic notions are explained.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, CA, 94720-3840, USA

    James Freitag

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  1. James Freitag
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Correspondence to James Freitag.

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Supported by NSF Grant DMS-1204510.

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Freitag, J. Isogeny in superstable groups. Arch. Math. Logic 53, 449–461 (2014). https://doi.org/10.1007/s00153-014-0373-z

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  • DOI: https://doi.org/10.1007/s00153-014-0373-z

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