Geodesic
On groups with almost perfect involution
Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 183-190

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The theorems of Jordan, Frobenius, M. Hall, Brauer–Suzuki–Wall, Shunkov, Mazurov, and Belyaev are generalized. 
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A. I. Sozutov. On groups with almost perfect involution. Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 183-190. http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a13/