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. 
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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/

[1] A. L. Mylnikov, “Konechnye perekruchennye gruppy”, Sib. matem. zh., 48:2 (2007), 369–375 | MR

[2] M. Aschbacher, “Near subgroups of finite groups”, J. Group Theory, 1:2 (1998), 113–129 | DOI | MR | Zbl

[3] A. L. Mylnikov, “Konechnye minimalnye neperekruchennye gruppy”, Vestnik Krasnoyarskogo gos. un-ta, 2005, no. 1, 71–76

[4] A. L. Mylnikov, “Abelevy perekruchennye gruppy”, Matem. sistemy, 3, Krasnoyarskii gos. agrar. un-t., Krasnoyarsk, 2005, 59–61

[5] A. L. Mylnikov, “Nilpotentnost kommutanta konechnoi perekruchennoi gruppy”, Sib. matem. zh., 47:5 (2006), 1117–1127 | MR

[6] A. L. Mylnikov, “O stupeni razreshimosti konechnoi perekruchennoi gruppy”, Vestnik Krasnoyarskogo gos. un-ta, 2006, no. 1, 61–67

[7] D. Gorienstein, Finite groups, Harper and Row, New York, 1968 | MR

[8] D. V. Veprintsev, A. L. Mylnikov, “Involyutivnaya dekompozitsiya gruppy i skruchennye podmnozhestva s malym kolichestvom involyutsii” (to appear)