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.


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
Full Text: DOI


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