Loops and the Lagrange property

Details Loops and the Lagrange property Loops and the Lagrange property

2002-05-13

arxiv.org/abs/math/0205141v1

Results Math. 43 (2003), no. 1-2, 74--78

Mathematics

Group Theory

4 pages, LaTeX2e, uses natbib.sty, submitted to Results in Mathematics

Scientific paper

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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