Automorphism groups of semigroups of upfamilies

2019 ◽  
Vol 13 (05) ◽  
pp. 2050099
Author(s):  
Volodymyr M. Gavrylkiv
Keyword(s):  
Binary Operation ◽  
Automorphism Groups ◽  
Left Zero

A family [Formula: see text] of nonempty subsets of a set [Formula: see text] is called an upfamily if for each set [Formula: see text] any set [Formula: see text] belongs to [Formula: see text]. The extension [Formula: see text] of [Formula: see text] consists of all upfamilies on [Formula: see text]. Any associative binary operation [Formula: see text] can be extended to an associative binary operation [Formula: see text]. In the paper, we study automorphisms of extensions of groups, finite monogenic semigroups, null semigroups, right zero semigroups and left zero semigroups. Also, we describe the automorphism groups of extensions of some semigroups of small cardinalities.

Automorphism groups with some finiteness conditions

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Konrad Pióro
Keyword(s):  
Lower Bound ◽  
Binary Operation ◽  
Automorphism Groups ◽  
The Other ◽  
Finiteness Conditions ◽  
Other Hand ◽  
The Right

AbstractAll considered groups are torsion or do not contain infinitely generated subgroups. If such a groupNext, we show that ifThe Birkhoff’s construction can be slightly modified so as to obtain a smaller set of operations. In fact, it is enough to take the right multiplications by generators. Moreover, we show that this is the best possible lower bound for the number of unary operations in the case of groups considered here. If we admit non-unary operations, then for finite and countable groups we can reduce the number of operations to one binary operation. On the other hand, if

Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

2020 ◽  
Vol 51 (4) ◽  
pp. 1919-1930
Author(s):  
Masoumeh Akbarizadeh ◽  
Mehdi Alaeiyan ◽  
Raffaele Scapellato
Keyword(s):  
Automorphism Groups

Using binary operations to construct a transitive set of block transformations

2020 ◽  
Vol 30 (6) ◽  
pp. 375-389
Author(s):  
Igor V. Cherednik
Keyword(s):  
Binary Operation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Binary Operations ◽  
The Family ◽  
Transitive Set ◽  
Necessary And Sufficient

AbstractWe study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Certain characterizations of varieties of bands

1988 ◽  
Vol 31 (2) ◽  
pp. 301-319 ◽  
Author(s):  
J. A. Gerhard ◽  
Mario Petrich
Keyword(s):  
Rectangular Band ◽  
Simple System ◽  
Left Zero ◽  
Green’S Relations ◽  
Transformation Semigroups ◽  
Lattice Of Varieties ◽  
Green's Relations ◽  
The World ◽  
New System

The lattice of varieties of bands was constructed in [1] by providing a simple system of invariants yielding a solution of the world problem for varieties of bands including a new system of inequivalent identities for these varieties. References [3] and [5] contain characterizations of varieties of bands determined by identities with up to three variables in terms of Green's relations and the functions figuring in a construction of a general band. In this construction, the band is expressed as a semilattice of rectangular bands and the multiplication is written in terms of functions among these rectangular band components and transformation semigroups on the corresponding left zero and right zero direct factors.

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

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