Related papers: Symmetry groups of Boolean Functions

A.A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to 3 over a commutative ring with unity is normal in the general linear group of same size.…

Let S be a principally embedded sl_2 subalgebra in sl_n for n > 2. A special case of results of the third author and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite-dimensional irreducible sl_n…

We define an extended Bloch group and show it is isomorphic to $H_3(PSL(2,C)^\delta;Z)$. Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger-Simons class on this homology group. It also…

We show that every action of a smooth algebraic group on a variety admits a normal projective model. Along the way, we present new proofs of some basic results on algebraic transformation groups, including Weil's regularization theorem.

A famous conjecture attributed to Dardano-Dikranjan-Rinauro-Salce states that any uniformly fully inert subgroup of a given group is commensurable with a fully invariant subgroup (see, respectively, [5] and [6]). In this short note, we…

This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of…

Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems and to provide solutions equivalent to the Bethe ansatz. The method is illustrated on the 1D Heisenberg ferromagnet whose symmetry…

We say a group is finitely annihilated if it is the set-theoretic union of all its proper normal finite index subgroups. We investigate this new property, and observe that it is independent of several other well known group properties. For…

Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is classical, employing well-known results from congruence function field theory.

We show that a Borel action of a standard Borel group which is isomorphic to a sum of a countable abelian group with a countable sum of real lines and circles induces an orbit equivalence relation which is hypersmooth, i.e., Borel reducible…

We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.

Refining a result of Erdos and Mays, we give asymptotic series expansions for the functions $A(x)-C(x)$, the count of $n\leq x$ for which every group of order $n$ is abelian (but not all cyclic), and $N(x)-A(x)$, the count of $n\leq x$ for…

It is well known that Euler experimentally discovered the functional equation of the Riemann zeta function. Indeed he detected the fundamental $s\mapsto 1-s$ invariance of $\zeta(s)$ by looking only at special values. In particular, via…

We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$. We produce partial results for abelian varieties over a general finite…

Let $a(n)$ denote the number of non-isomorphic abelian groups with $n$ elements. In 1991 Ivi\'{c} proved an asymptotic formula of the sum $\sum_{n\leq x} a(n+ a(n)).$ In this paper, we will prove a sharper asymptotic formula for this sum.

The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism…

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above…

We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.

We show that integral representation of universal volume function of compact simple Lie groups gives rise to six analytic functions on $CP^2$, which transform as two triplets under group of permutations of Vogel's projective parameters.…

We prove asymptotically isometric, coarsely geodesic metrics on a toral relatively hyperbolic group are coarsely equal. The theorem applies to all lattices in SO(n,1). This partly verifies a conjecture by Margulis. In the case of hyperbolic…