Related papers: Nilpotent Steiner loops of class 2
We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.
We classify the nilpotent Lie rings of order $p^8$ with maximal class for $p \ge 5$. This also provides a classification of the groups of order $p^8$ with maximal class for $p \ge 11$ via the Lazard correspondence.
We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.
The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the…
This paper initiates the study of effective twisted conjugacy separability for finitely generated groups, which measures the complexity of separating distinct twisted conjugacy classes via finite quotients. The focus is on nilpotent groups,…
In this paper, we classify finite-dimensional nilpotent Lie superalgebras of superbreadth at most two.
In this paper, nilpotent n-Lie algebras of dimension n + 3 as well as nilpotent n-Lie algebras of class 2 and dimension n + 4 are classified.
We classify the module categories over the double (possibly twisted) of a finite group.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
We characterize those graphs which correspond to a rigid 2-step nilpotent Lie algebra in the variety of at most 2-step nilpotent Lie algebras.
We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.
In this paper, we investigate nilpotent Lie algebras $ L $ of nilpotency class $3 $ and provide a complete classification of those satisfying $ \dim L^2 = 3 $ and $Z(L) = L^3 \cong A(2). $ Furthermore, we explicitly characterize the…
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
Let $G$ be a finite group. In this short note, we give a criterion of nilpotency of $G$ based on the existence of elements of certain order in each section of $G$.
We show presentations of automata groups generated by Cayley machines of finite groups of nilpotency class two and these automata groups are all cross-wired lamplighters.
In this paper we study contact structure on 2-step nilpotent, Heisenberg type Lie groups. We decompose this Lie groups to center and orthogonal complement, then investigate properties of both orthogonal Lie subgroups. Finally, we provide a…
In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.
The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given…
We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras
We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…