Some Notes on the Baer-Invariant of a Nilpotent Product of Groups

Communications in Algebra

2006

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In this paper, we present an explicit structure for the Baer invariant of a free nilpotent group ( the n-th nilpotent product of the infinite cyclic group, Z n * Z n * . . . n * Z) with respect to the variety of polynilpotent groups of class row (c, 1), N c,1 , for all c > 2n − 2. In particular, an explicit structure of the Baer invariant of a free abelian group with respect to the variety of metabelian groups will be presented.

Section: Introductionmentioning

confidence: 99%

On Polynilpotent Multipliers of Free Nilpotent Groups

Parvizi

Communications in Algebra

2006

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“…In 2001, the first author [11] found a structure similar to Haebich's type for the c-nilpotent multiplier of a nilpotent product of a family of cyclic groups. The c-nilpotent multiplier of a free product of some cyclic groups was studied by the first author [12] in 2002.…”

Section: Introductionmentioning

confidence: 89%

Some Baer invariants of free nilpotent groups

Parvizi

2007

Journal of Algebra

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We present an explicit structure for the Baer invariant of a free nth nilpotent group (the nth nilpotent product of infinite cyclic groups, Z n * Z n * · · · n * Z) with respect to the variety V with the set of words V = {[γ c 1 +1 , γ c 2 +1 ]}, for all c 1 c 2 and 2c 2 − c 1 > 2n − 2. Also, an explicit formula for the polynilpotent multiplier of a free nth nilpotent group is given for any class row (c 1 , c 2 , . . . , c t ), where c 1 n.

“…(ii) If V is the variety of nilpotent groups of class at most n, N n , then main results of the second author [9] are obtained by Theorem 2.9 and Corollary 2.11.…”

Section: And the Fact Thatmentioning

confidence: 98%

“…Then the second author [9] extended the result to find a homomorphic image with a structure similar to Haebich's type for the c-nilpotent multiplier of a nilpotent product of a family of groups.…”

Section: Introductionmentioning

confidence: 95%

On nilpotent multipliers of some verbal products of groups

Hokmabadi

2008

Journal of Algebra

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The paper is devoted to finding a homomorphic image for the cnilpotent 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 rt , 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.