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Frattini Subobjects and Extensions in Semi-Abelian Categories

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Abstract

The purpose of this paper is to introduce Frattini theory in semi-abelian categories. We extend several basic group-theoretic results about Frattini subgroups and Frattini extensions, specifically selected from an article of Moori and Rodrigues, to a categorical context involving either Hoehnke radicals or our notion of Frattini subobjects.

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Acknowledgements

Partially supported by the South African National Research Foundation and Georgian Shota Rustaveli National Science Foundation Grant DI/18/5-113/13.

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Authors and Affiliations

  1. University of Cape Town, Rondebosch, 7401, South Africa

    George Janelidze

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  1. George Janelidze
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Correspondence to George Janelidze.

Additional information

Communicated by Themba Dube.

Dedicated to Jamshid Moori on the occasion of his 70th birthday.

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Janelidze, G. Frattini Subobjects and Extensions in Semi-Abelian Categories. Bull. Iran. Math. Soc. 44, 291–304 (2018). https://doi.org/10.1007/s41980-018-0020-2

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