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Groups with elementary Abelian centralizers of involutions. (Russian, English) Zbl 1155.20028
Algebra Logika 46, No. 1, 75-82 (2007); translation in Algebra Logic 46, No. 1, 46-49 (2007).
Summary: An involution \(i\) of a group \(G\) is said to be almost perfect in \(G\) if any two involutions of \(i^G\) the order of the product of which is infinite are conjugated via a suitable involution in \(i^G\). We generalize a known result by Brauer, Suzuki, and Wall concerning the structure of finite groups with elementary Abelian centralizers of involutions to groups with almost perfect involutions.

20E34 General structure theorems for groups
20E07 Subgroup theorems; subgroup growth
20E45 Conjugacy classes for groups
20F24 FC-groups and their generalizations
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