We classify irreducible representations of finite W-algebra for the queer Lie superalgebra Q(n) associated with principal nilpotent coadjoint orbits. use this classification and our previous results to obtain a finite-dimensional super Yangian YQ(1).

‎let $g$ be a finite group and $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎in this paper‎, ‎all nilpotent groups $g$ with $nu(g)=3$ are classified‎.

The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup.

We show that ω-categorical rings with NIP are nilpotent-by-finite. We prove that an ω-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an ω-categorical group with at least one strongly regular type is abelian. Moreover, we get that each ω-categorical, characteristically simple p-group with NIP has an infinite, definable abelian subgroup. Assuming additionally the e...

For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...

This paper gives a characteristic condition of finite nilpotent group under the assumption that all minimal subgroups of G are well-suited in G.

According to a folklore result, every regular map on an orientable surface with abelian automorphism group belongs to one of three infinite families of maps with one or two vertices. Here we deal with regular maps whose automorphism group is nilpotent. We show that each such map decomposes into a direct product of two maps H×K, where Aut(H) is a 2-group and K is a map with a single vertex and a...

We prove that a torsion group G with all subgroups subnormal is a nilpotent group or G = N(A1×· · ·×An) is a product of a normal nilpotent subgroup N and pi -subgroups Ai , where Ai = A (i) 1 · · ·A (i) mi G , A (i) j is a Heineken–Mohamed type group, and p1, . . . , pn are pairwise distinct primes (n ≥ 1; i = 1, . . . , n; j = 1, . . . ,mi and mi are positive integers).

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h ∈ H. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with [F ′, H] = 1. In case where CG(F ) = 1 we prove that the groups G and CG(H) have the same nilpotent length un...

A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the small class case. The approach is also used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also prove a necessary condition for the capability of an arbitrary p-group of ...