The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion sys- tems and finite p J-core-free p-constrained minimal...The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups.展开更多
Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions ...Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.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
基金Supported by the National 973 Project (452101650122) and the National Natural Science Foundation of China (11201194, 11301393). In addition, the second author was supported by the doctoral foundation of Jiangxi Normal University.
文摘The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups.
基金Foundation item:The NNSF(10571026)of China,the NSF(BK2005207)of Jiangsu Provincethe Specialized Research Fund(20060286006)for the Doctoral Program of Higher Education.
文摘Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.
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).