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Ideals in intra-regular left almost semigroups
LA-semigroups intra-regular LA-semigroups and (1, 2)-ideals
2011/2/28
In this paper, we have introduced the notion of (1, 2)-ideal in an LA-semigroup and shown that (1, 2)-ideal and two-sided ideal coincide in an intra-regular LA-semigroup.
Vector Groupoids
Brandt groupoid vector groupoid
2011/2/24
The main purpose of this paper is to study the vector groupoids.This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible. The new c...
We give a list of finite groups containing all finite groups G such that the group of units ZG∗ of the integral group ring ZG is subgroup separable. There are only two types of these groups G fo...
Cluster categories were defined in [BMRRT] in order to use categorical methods to give a conceptual model for the combinatorics of cluster algebras, as defined by Fomin and Zelevinsky [FZ].
Nonfree Actions of Countable Groups and their Characters
Nonfree actions lattice of subgroups characters factor representa-tions
2011/2/24
We introduce a number of definitions of nonfree actions of groups. The most important of them is that of a totally nonfree action; it is naturally related to the theory of characters of groups and the...
Explicit computation of the index of a positive outer automorphism of the free group
Explicit computation index of positive outer automorphism
2011/2/21
We give an algorithm for finding the index of a positive outer au-tomorphism of the free group, and prove the algorithm exits in a finite time.
Rational subsets of groups
Free groups inverse automata Stallings automata rational subsets
2011/3/2
Over the years, finite automata have been used effectively in the theory of infinite
groups to represent rational subsets.
Some Inequalities for Nilpotent Multipliers of Finite Groups
Nilpotent multiplier Finite p-group Inequality
2011/2/21
In this paper we present some inequalities for the order, the expo-nent and the number of generators of the c-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups o...
At which points exactly has Lebesgue's singular function the derivative zero ?
Takagi’s function Lebesgue’s singular function Nowhere-differentiable function
2011/2/28
Let La(x) be Lebesgue’s singular function with a real parameter a (0 < a < 1, a 6= 1/2). As is well known, La(x) is strictly increasing and has a derivative equal to zero almost everywhere.
On the Order of Schur Multipliers of Finite Abelian p-Groups
Schur multiplier Abelian p- group
2011/2/21
Let G be a finite p-group of order pn with |M(G)| = p n(n−1) 2 −t,where M(G) is the Schur multiplier of G. Ya.G. Berkovich, X. Zhou,and G. Ellis have determined the structure of G when t =...
The automorphism group of the group of unitriangular matrices over a field
automorphism group group of unitriangular matrices
2011/2/28
This paper finds the generators of the automorphism group of the group of unitriangular matrices over a field. Most of this paper is an exposition of the work of V.M. Lev˘chuk, part of which is i...
New series in the Johnson cokernels of the mapping class groups of surfaces
New series Johnson cokernels mapping class groups of surfaces
2011/1/20
Let g,1 be a compact oriented surface of genus g with one boundary component,andMg,1 its mapping class group. Morita showed that the image of the k-th Johnson homomorphism M
k of Mg,1 is contained ...
Hemisystems of small flock generalized quadrangles
Hemisystem flock generalized quadrangle partial quadrangle
2011/2/22
In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order (52, 5) and give numerous further examples of hemisystems in al...
Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups
Outer Commutator Multiplier Capability of Finitely Generated Abelian Groups
2011/2/21
We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety [Nc1 ,Nc2], for all c2 ≤ c1 ≤ 2c2.
Let v = (v1, · · · , ve+s) be a set of vectors of Ne, and assume that ve+k is not in the group generated by v1, . . . , ve+k−1 for all k = 1, · · · , s. The aim of this paper is to give a formul...