Complementability conditions for a periodic almost solvable subgroup in the group containing it
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It is proved that if every prime Sylow subgroup of a periodic almost solvable (more generally, periodic W0-) subgroup H of a group G has a complement in G and if, moreover, H is at most countable and the set Π(H) is finite, the subgroup H itself possesses a complement in G.
KeywordsSylow Subgroup Complementability Condition Solvable Subgroup
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