On a strongly embedded infinitely isolated subgroup of a periodic group
This is a continuation of a paper by the author and \textit{V. P. Shunkov} [Algebra Logika 21, 647-669 (1982; Zbl 0536.20022)]. It gives a further criterion for the non-simplicity of a group G having a strongly embedded infinite isolated subgroup H. It is assumed that H contains infinitely many involutions such that G has an involution for which the centralizer of any infinite subgroup without elements of order 2 contains a non- trivial element whose centralizer in that subgroup is infinite. Suppose also that H has a non-trivial element b that is strictly real relative to a certain involution of G whose centralizer in G is not contained in H. Then G has a normal Abelian subgroup B between H and \(\) that does not contain involutions such that all elements of B are strictly real relative to any involution in G. Also, G is the product of the centralizer of B and that of any involution in G, and the Sylow 2- subgroups are either locally cyclic or generalized quaternion groups.
strongly embedded infinite isolated subgroup
scientific article; zbMATH DE number 3869597