Related papers: A characterization of elementary abelian 2-groups
We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group $G$. In particular, we determine the threshold $p_c \approx \sqrt{\log n / n}$ above which, with high probability as $|G| \to \infty$,…
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.
In this paper we study sum-free sets of order $m$ in finite Abelian groups. We prove a general theorem on 3-uniform hypergraphs, which allows us to deduce structural results in the sparse setting from stability results in the dense setting.…
The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.
Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
A maximal abelian normal subgroup A in a nilpotent group N is self-centralizing. This makes their role an important one in determining the structure of the nilpotent group. For example if A is finite then N is also finite. In the free…
It is proved that any infinite Abelian topological group of prime exponent has an infinite maximally almost periodic subgroup.
We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\aleph_0}$ many continuous ergodic invariant random…
We define and study in-depth the so-called completely inert and uniformly completely inert subgroups of Abelian groups. We curiously show that a subgroup is completely inert exactly when it is characteristically inert. Moreover, we prove…
It is known that every torsion-free abelian group of finite rank has a maximal completely decomposable summand that is unique up to isomorphism. We show that groups of infinite rank need not have maximal completely decomposable summands,…
We prove an elementary additive combinatorics inequality, which says that if $A$ is a subset of an Abelian group, which has, in some strong sense, large doubling, then the difference set A-A has a large subset, which has small doubling.
We recall and delve into the different characterizations of the depth of an affine semigroup ring, providing an original characterization of depth two in three and four dimensional cases which are closely related to the existence of a…
We give a characterization of the finite groups having nilpotent or abelian Hall $\pi$-subgroups which can easily be verified from the character table.
Let $A$ be an infinitely generated free abelian group. We prove that the automorphism group $\aut A$ first-order interprets the full second-order theory of the set $|A|$ with no structure. In particular, this implies that the automorphism…
Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…
We build two non-abelian CSA-groups in which maximal abelian subgroups are conjugate and divisible.
It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…
Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for…
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…