Finite groups with involution whose centralizer has a quotient group isomorphic with \({\mathcal L}_ 2(2^ n)\). (English. Russian original) Zbl 0598.20014

Algebra Logic 21, 267-272 (1983); translation from Algebra Logika 21, No. 4, 402-409 (1982).
Main result: Let G be a finite group, z be an involution in G, whose centralizer is an extension of a 2-subgroup \({\mathcal Q}\) by \(L_ 2(2^ n)\), \(n\geq 2\). Let us assume in addition that the centralizer of an element of order 3 of C(z) in \({\mathcal Q}\) is a cyclic subgroup, which is normal in C(z). Then if z is a central involution, then \(G=O(G)C(z)\) or \(G\simeq J_ 1\), and if z is noncentral, then \(z\not\in G'\).


20D05 Finite simple groups and their classification
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