The Baer Invariant of Semidirect and Verbal Wreath Products of Groups

Details The Baer Invariant of Semidirect and Verbal Wreath Products of Groups The Baer Invariant of Semidirect and Verbal Wreath Products of Groups

2011-03-26

arxiv.org/abs/1103.5160v1

International Journal of Mathematics, Game Theory and algebra, 15:4 (2006) 387-402

Mathematics

Group Theory

28 pages

Scientific paper

W. Haebich (1977, Journal of Algebra {\bf 44}, 420-433) presented some formulas for the Schur multiplier of a semidirect product and also a verbal wreath product of two groups. The author (1997, Indag. Math., (N.S.), {\bf 8}({\bf 4}), 529-535) generalized a theorem of W. Haebich to the Baer invariant of a semidirect product of two groups with respect to the variety of nilpotent groups of class at most $c\geq 1,\ {\cal N}_c$. In this paper, first, it is shown that ${\cal V}M(B)$ and ${\cal V}M(A)$ are direct factors of ${\cal V}M(G)$, where $G=B\rhd

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