Related papers: Reality of Unipotent elements in Classical Lie Gro…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

For an element $g$ in a group $X$, we say that $g$ has 2-part order $2^{a}$ if $2^{a}$ is the largest power of 2 dividing the order of $g$. We prove lower bounds on the proportion of elements in finite classical groups in odd characteristic…

New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

Let $\F$ be a field with a non-trivial involution $c: \alpha \to \alpha^c$. An element $g \in {\rm GL}_n(\F)$ is called $c$-real if it is conjugate to $(g^c)^{-1}$. We prove that for $n \geq 2$, $g \in {\rm GL}_n(\F)$ is $c$-real if and…

At present many of the endeavours in physics are made to recognize in quantum substance classical reality, time, subjectivity, consciousness and many other physical and nonphysical features. The purpose of these remarks is to draw attention…

Right feeble groups are defined as groupoids $(X,*)$ such that (i) $x, y\in X$ implies the existence of $a, b \in X$ such that $a*x = y$ and $b*y = x$. Furthermore, (ii) if $x, y, z \in X$ then there is an element $w\in X$ such that…

We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a…

The aim of the paper is to popularise nilpotent Lie groups (notably the Heisenberg group and alike) in the context of Clifford analysis and related models of mathematical physics. It is argued that these groups are underinvestigated in…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.

Let $n \in \NN$ and let $q=p^r$ be an odd prime power. Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ with $R/J(R) \simeq GF(q)$. We study the conjugation action of the group of all unipotent elements in the…

Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity element. This particular article focuses on an examination of…

We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.

In this paper we construct compact forms associated with a complex Lie supergroup with Lie superalgebra of classical type.

The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…

In this paper we perform Lie group analysis of systems of partial differential equations which describe different cases of classical plasma equilibria, and find groups of transformations admitted by those equations in several important…

In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…

We study relatively minimal subgroups in topological groups. We find, in particular, some natural relatively minimal subgroups in unipotent groups which are defined over "good" rings. By "good" rings we mean archimedean absolute valued (not…

A word $w$ is concise in a class of groups $\mathcal{C}$ if, for every group $G$ in $\mathcal{C}$, the verbal subgroup $w(G)$ is finite whenever $w$ takes only finitely many values in $G$. This notion can be naturally extended to…