Results 191 to 200 of about 1,310,702 (229)

Commutative ideal extensions of abelian groups

ACM SIGSAM Bulletin, 1999
An element \(x\) in a semigroup \(S\) is Archimedean if for every \(y\in S\) there exist a nonnegative integer \(k\) and \(z\in S\) such that \(kx=y+z\). A commutative semigroup \(E\) is an ideal extension of an Abelian group if and only if \(E\) has an element that is Archimedean and idempotent.
Juan Ignacio García-García, Pedro A. García-Sánchez, José Carlos Rosales   +2 more
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The Little Group Method for Abelian Extensions

2022
In this chapter we study the representation theory of the class of groups G with a normal subgroup N such that the following conditions are satisfied: (formula presented).
Ceccherini-Silberstein T., Scarabotti F., Tolli F.   +2 more
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A note on abelian extensions

Wuhan University Journal of Natural Sciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu, Chuxiong, Fan, Yun
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Distribution of Discriminants of Abelian Extensions

Proceedings of the London Mathematical Society, 1989
In this paper, class field theory is used to determine the distribution of the relative discriminants of all Galois extensions of a given global field k with Galois group isomorphic to a given finite abelian group G. In the case that the base field has characteristic \(p>0\), the results established assume that p does not divide the order of G.
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Ramification in Elementary Abelian Extensions

Journal of Mathematical Sciences, 2014
Let \(K\) be a complete discrete valuation field \(K\) with imperfect residue field \(\bar{K}\), valuation \(v_K\) and maximal ideal \({\mathfrak m}_K\). It is assumed that \([\bar{K}:\bar{K}^p]=p\). For a natural number \(i\), let \(K_i\) be the composite of all extensions \(L/K\) such that \(L/K\) is given by the equation \(x^p-x=a, a\in{\mathfrak m ...
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HOMOLOGY OF FREE ABELIANIZED EXTENSIONS OF GROUPS

Mathematics of the USSR-Sbornik, 1992
Let \(G\) be a group presented as a factor group \(G = F/N\) of a free group \(F\). Let \(\Phi = F/N'\), which is known as a free abelian extension of \(G\). Ground breaking work on the homology groups of \(\Phi\) with trivial integer coefficients was done by the second author [Commun. Algebra 16, No. 12, 2447-2533 (1988; Zbl 0682.20038)].
Kovács, L. G., Kuz'min, Yu. V., Stöhr, R.   +2 more
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Extensions of Abelian Groups

1968
The object of extension, theory is to give a survey of the possible abstractly different extensions of a group T by a group K. Our solution consists in exhibiting a representative family of extensions of T by K supplemented by a criterion for the isomorphy of groups of this family. We consider arbitrary reduced groups T and arbitrary groups K.
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Semigroup extensions of Abelian topological groups

Semigroup Forum, 2018
In the paper it is stated that a topological group is called \textit{absolutely closed} if it is closed in every topological group containing it as a subgroup; and a topological group is absolutely closed if and only if it is complete [\textit{D. Raikov}, Izv. Akad. Nauk SSSR, Ser. Mat. 10, 513--528 (1946; Zbl 0061.04206)]. Given a topological group $G$
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A New Invariant for Tame, Abelian Extensions

Journal of the London Mathematical Society, 1990
Suppose \(K| \mathbb Q\) is tame and abelian with \(\Gamma =\text{Gal}(K| \mathbb Q)\). Let \(\mathfrak O_ K\) denote the ring of algebraic integers in \(K\). Then a basis of \(\mathfrak O_ K\) exists (over \(\mathbb Z\)), consisting of the conjugates of a single element, that is \({\mathfrak O}_ K=a.\mathbb Z\Gamma\) for some \(a\in {\mathfrak O}_ K\).
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Abelian Extensions with Restricted Ramification — Abelian Closure

2003
This chapter deals with the correspondence of class field theory both for finite and infinite extensions; this second aspect, obtained by limiting processes, will enable us to understand the structure of the maximal abelian extension of a number field K (Section 4 of the present chapter).
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