Related papers: A characterization of elementary abelian 2-groups

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…

Let A, B and S be three subsets of a finite Abelian group G. The restricted sumset of A and B with respect to S is defined as A\wedge^{S} B= {a+b: a in A, b in B and a-b not in S}. Let L_S=max_{z in G}| {(x,y): x,y in G, x+y=z and x-y in…

A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson…

A finite subset $A$ of an abelian group $G$ is said to be zero-free if the identity element of $G$ cannot be written as a sum of distinct elements from $A$. In this article we study the structure of zero-free subsets of $Z/pZ$ the…

Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The invariants of such groups determined by their group algebras over the field of two elements are given in the paper.

Let $F$ be a finite field of characteristic $p>0$ with $q = p^{n}$ elements. In this paper, a complete characterization of the unit groups $U(FG)$ of group algebras $FG$ for the abelian groups of order $32$, over finite field of…

An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite,…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

Elementarily free groups are the finitely generated groups with the same elementary theory as free groups. We prove that elementarily free groups are subgroup separable, answering a question of Zlil Sela.

We study the Ap\'ery set of good subsemigoups of $\mathbb N^2$, a class of semigroups containing the value semigroups of curve singularities with two branches. Even if this set in infinite, we show that, for the Ap\'ery set of such…

Given a prime $p$, we construct a permutation group containing at least $p^{p-2}$ non-conjugated regular elementary abelian subgroups of order $p^3$. This gives the first example of a permutation group with exponentially many non-conjugated…

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…

For an arbitrary ring $A$, we study the abelianization of the elementary group $\textrm{E}_2(A)$. In particular, we show that for a commutative ring $A$ there exists an exact sequence \[ K_2(2,A)/C(2,A) \to A/M \to…

In this paper we characterize all of Cayley graphs on dihedral groups with metric dimension two.

We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…

For Abelian p-groups, Goldsmith, Salce, et al., introduced the notion of minimal full inertia. In parallel to this, we define the concept of minimal characteristic inertia and explore those p-primary Abelian groups having minimal…

We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.

A subset $A$ of a finite abelian group is called $(k,\ell)$-sum-free if $kA \cap \ell A=\emptyset.$ In this paper, we extend this concept to compact abelian groups and study the question of how large a measurable $(k,\ell)$-sum-free set can…

The fine abelian group gradings on the simple exceptional classical Lie superalgebras over algebraically closed fields of characteristic 0 are determined up to equivalence.