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 $$z\not\in G'$$.

MSC:

 20D05 Finite simple groups and their classification

Keywords:

centralizer; central involution; $$J_ 1$$
Full Text:

References:

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