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Polar Decomposition of Locally Finite Groups

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Abstract

The study of loops as transversals in groups dates back to the works of Reinhold Baer. In the past few years there have been several papers using polar decomposition in linear algebra in order to construct Bruck loops. In this paper we generalize the notion of polar decomposition to any arbitrary group, and we show that in any polar decomposition the binary operation “inherited” from the group leads to the construction of a Bruck loop.

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  1. Department of Mathematics, North Dakota State University, Fargo, ND, 58105, USA

    Tuval Foguel

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  1. Tuval Foguel
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Correspondence to Tuval Foguel.

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Foguel, T. Polar Decomposition of Locally Finite Groups. Results. Math. 42, 69–73 (2002). https://doi.org/10.1007/BF03323554

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