Loops and the Lagrange Property
Copyright policy )Loops and the Lagrange Property
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.
4 pages, LaTeX2e, uses natbib.sty, submitted to Results in Mathematics
- Universiti Sains Malaysia Malaysia
- Temple University United States
- Eastern Michigan University United States
- Iowa State University United States
Lagrange property, finite loops, Loops, quasigroups, varieties of loops, commutative Moufang loops, 20N05, Group Theory (math.GR), simple loops, FOS: Mathematics, Bol loops, Mathematics - Group Theory, Paige loops
Lagrange property, finite loops, Loops, quasigroups, varieties of loops, commutative Moufang loops, 20N05, Group Theory (math.GR), simple loops, FOS: Mathematics, Bol loops, Mathematics - Group Theory, Paige loops
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