查看更多>>摘要:Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let Θm(n)=A×(α)be the split extension of A by an automorphismα which is a cyclic permutation of the direct components twisted by a rational integer m.Then Θm(n)is an infinite soluble group.In this paper,the residual finiteness of Θm(n)is investigated.
查看更多>>摘要:We obtain a complete characterization of the structure of a finite group G in which every maximal subgroup is nilpotent or a TI-subgroup or has order p'for any fixed prime divisor p of|G|.Moreover,we show that there exists at most one prime divisor q of|G|| such that G is neither q-niilpotent nor q-closed.
查看更多>>摘要:We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields.We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can be separated by classical conjugation invariants defined by characteristic polynomials.We also find a gen-erating set for the vanishing ideal of these orbits.