scholarly journals The multiple holomorph of a semidirect product of groups having coprime exponents

2020 ◽  
Vol 115 (1) ◽  
pp. 13-21
Author(s):  
Cindy Tsang
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

scholarly journals Supramenable groups and partial actions

2016 ◽  
Vol 37 (5) ◽  
pp. 1592-1606 ◽  
Author(s):  
EDUARDO P. SCARPARO
Keyword(s):  
Semidirect Product ◽  
Crossed Product ◽  
Probability Measures ◽  
Crossed Products ◽  
Hausdorff Spaces ◽  
Tracial States ◽  
Product Of Groups

We characterize supramenable groups in terms of the existence of invariant probability measures for partial actions on compact Hausdorff spaces and the existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a $\text{C}^{\ast }$-algebra by a semidirect product of groups into two iterated partial crossed products. However, we give conditions which ensure that such decomposition is possible.

scholarly journals Is a semidirect product of groups necessarily a group?

1993 ◽  
Vol 118 (3) ◽  
pp. 689-689 ◽  
Author(s):  
Gary F. Birkenmeier ◽  
C. Brad Davis ◽  
Kevin J. Reeves ◽  
Sihai Xiao
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

Application of the Semidirect Product of Groups

1971 ◽  
Vol 12 (2) ◽  
pp. 314-314 ◽  
Author(s):  
Robert Geroch ◽  
E. T. Newman
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

scholarly journals On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

Topological Left Amenability of Semidirect Products

1981 ◽  
Vol 24 (1) ◽  
pp. 79-85 ◽  
Author(s):  
H. D. Junghenn
Keyword(s):  
Large Class ◽  
Semidirect Product ◽  
Locally Compact ◽  
Semidirect Products ◽  
Topological Semigroups

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.

scholarly journals Product of the GeneralizedL-Subgroups

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Dilek Bayrak ◽  
Sultan Yamak
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Product Of Groups

We introduce the notion of(λ,μ)-product ofL-subsets. We give a necessary and sufficient condition for(λ,μ)-L-subgroup of a product of groups to be(λ,μ)-product of(λ,μ)-L-subgroups.

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