In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety re...In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.展开更多
The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality o...The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.展开更多
文摘In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.
基金Supported by Grant No.RD-08-82/03.02.2016 of Shumen University
文摘The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.
