Weak Identities in Finitely Generated Groups
نویسنده
چکیده
In this article we introduce the notion of weak identities in a group and study their properties. We show that weak identities have some similar properties to ordinary ones. We use this notion to prove that any finitely generated solvable discriminating group is abelian, which answers a question raised in [3].
منابع مشابه
On Regularity of Acts
In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...
متن کاملA characterization of finitely generated multiplication modules
Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...
متن کاملOn a Semigroup Variety of György Pollák
Let P be the variety of semigroups defined by the identity xyzx ≈ x. By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains...
متن کاملRational Polyhedra and Projective Lattice-ordered Abelian Groups with Order Unit
An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order unit, i.e., an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate every element of G. While every finitely generated projective unital l-...
متن کاملOn bounded weak approximate identities and a new version of them
In this paper, we give a short survey of results and problems concerning the notion of bounded weak approximate identities in Banach algebras. Also, we introduce a new version of approximate identities and give one illuminating example to show the difference.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003