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Minimal involution-free nongroup reduced twisted subsets. (English. Russian original) Zbl 1232.20030

Math. Notes 88, No. 6, 860-867 (2010); translation from Mat. Zametki 88, No. 6, 902-910 (2010).
Summary: A subset \(K\) of a group \(G\) is said to be twisted if \(1\in K\) and the element \(xy^{-1}x\) lies in \(K\) for any \(x,y\in K\). We study finite involution-free twisted subsets that are not subgroups but all of whose proper twisted subsets are subgroups. We also study the groups generated by such twisted subsets.

MSC:

20D60 Arithmetic and combinatorial problems involving abstract finite groups
20F05 Generators, relations, and presentations of groups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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References:

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