Abstract
The main result of the paper is the following theorem. Let G be a locally finite group having a four-subgroup V such that C G (V) is finite. Suppose that V contains two involutions v 1 and v 2 such that the centralizers C G (v 1) and C G (v 2) have finite exponent. Then G is almost locally soluble and [G, V]′ has finite exponent. Since [G, V] has finite index in G, the result gives a fairly detailed information about the structure of G.
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P. Shumyatsky was supported by CNPq-Brazil.
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Romano, E., Shumyatsky, P. On locally finite groups with a small centralizer of a four-subgroup. Arch. Math. 97, 1–10 (2011). https://doi.org/10.1007/s00013-011-0273-y
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DOI: https://doi.org/10.1007/s00013-011-0273-y