On nilpotent multipliers of some verbal products of groups

The paper is devoted to finding a homomorphic image for the c-nilpotent multiplier of the verbal product of a family of groups with respect to a variety V when V ⊆ N c or N c ⊆ V . Also a structure of the c-nilpotent multiplier of a special case of the verbal product, the nilpotent product, of cycli...

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Bibliographic Details
Published in:Journal of algebra 2008-10, Vol.320 (8), p.3269-3277
Main Authors: Hokmabadi, Azam, Mashayekhy, Behrooz
Format: Article
Language:English
Subjects:
Cyclic group
Nilpotent multiplier
Nilpotent product
Verbal product
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Summary:The paper is devoted to finding a homomorphic image for the c-nilpotent multiplier of the verbal product of a family of groups with respect to a variety V when V ⊆ N c or N c ⊆ V . Also a structure of the c-nilpotent multiplier of a special case of the verbal product, the nilpotent product, of cyclic groups is given. In fact, we present an explicit formula for the c-nilpotent multiplier of the nth nilpotent product of the group G = Z ∗ n ⋯ ∗ n Z ∗ n Z r 1 ∗ n ⋯ ∗ n Z r t , where r i + 1 divides r i for all i, 1 ⩽ i ⩽ t − 1 , and ( p , r 1 ) = 1 for any prime p less than or equal to n + c , for all positive integers n, c.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2008.07.013