The nil Hecke ring and singularity of Schubert varieties.
The nil-degree of a torsion-free Abelian group
The nilpotency of some groups with all subgroups subnormal.
Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.
The nilpotency of torsion-free rings with given type set
The Nonexistence of Certain Moufang Polygons.
The nonseparability of simply presented mixed groups
It is demonstrated that an isotype subgroup of a simply presented abelian group can be simply presented without being a separable subgroup. In particular, the conjecture based on a variety of special cases that Warfield groups are absolutely separable is disproved.
The Non-Solvable Hall Subgroups of the General Linear Group.
The normality of closures of conjugacy classes of matrices.
The Normalizer of the level (2,2)-Heisenberg Group.
The normalizer splitting conjecture for p-compact groups
Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group . We prove that for an odd prime p, the fibration has a section, which is unique up to vertical homotopy.
The notion of norm and the representation theory of orthogonal groups.
The number of commutative semigroups of order N.
The Number of Conjugacy Classes in a Finite Group.
The number of conjugacy classes in a finite nilpotent group
The number of conjugacy classes of elements of the Cremona group of some given finite order
This note presents the study of the conjugacy classes of elements of some given finite order in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if is even, or , and that it is equal to (respectively ) if (respectively if ) and to for all remaining odd orders. Some precise representative elements of the classes are given.
The number of finite groups whose element orders is given.
The number of indecomposable Schur rings over a cyclic 2-group.
The number of k-sums of abelian groups of order k
The number of minimal varieties of idempotent groupoids
The number of representations of a group induced from the irreducible representations of a normal subgroup.