Center of some solvable groups with one defining relation
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Necessary and sufficient conditions for the center of a metabelian group with one defining relation to be nontrivial are found. The center of such a group is described. The center of a group of the formF/N′〈g〉 F is studied under certain conditions. By means of a new technique, the recent result of A. F. Krasnikov and the author on the center of a group of the above form is sharpened.
Key wordsmetabelian group free group center of a group n-solvable group defining relations
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