Geodesic
Minimal non-group twisted subsets containing involutions
Algebra i logika, Tome 46 (2007) no. 4, pp. 459-482

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A subset $K$ of a group $G$ is said to be twisted if $1\in K$ and $xy^{-1}x\in K$ for any $x,y\in K$. We explore finite twisted subsets with involutions which are themselves not subgroups but every proper twisted subset of which is. Groups that are generated by such twisted subsets are classified.
Keywords: involution, twisted subset, twisted subgroup. 
@article{AL_2007_46_4_a3,
     author = {A. L. Myl'nikov},
     title = {Minimal non-group twisted subsets containing involutions},
     journal = {Algebra i logika},
     pages = {459--482},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_4_a3/}
}
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A. L. Myl'nikov. Minimal non-group twisted subsets containing involutions. Algebra i logika, Tome 46 (2007) no. 4, pp. 459-482. http://geodesic.mathdoc.fr/item/AL_2007_46_4_a3/