Subgroup Theorems for the Baer-Invariant of Groups

M. R. Jones and J. Wiegold (J. London Math. Soc. (2)6, 1973, 738) have shown that ifGis a finite group with a subgroupHof finite indexn, then thenth power of the Schur multiplier ofG,M(G)n, is isomorphic to a subgroup ofM(H). In this paper we prove a similar result for the centre by centre bywvariety of groups, wherewis any outer commutator word. Then using a result of M. R. R. Moghaddam (Arch. Math.33,1979, 504–511), we will be able to deduce a result of Schurʹs type with respect to the variety of nilpotent groups of class at mostc(c ≥ 1), whenc + 1 is any prime number or 4.