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Loops and the Lagrange property

Orin Chein·Michael K. Kinyon·Andrew Rajah·Petr Vojtechovsky
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Abstract

Let $\cF$ be a family of finite loops closed under subloops and factor loops. Then every loop in $\cF$ has the strong Lagrange property if and only if every simple loop in $\cF$ has the weak Lagrange property. We exhibit several such families, and indicate how the Lagrange property enters into the problem of existence of finite simple loops.

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Orin Chein, Michael K. Kinyon, Andrew Rajah, Petr Vojtechovsky. 2002-05-13. Loops and the Lagrange property. https://arxiv.org/abs/math/0205141

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