Search results for "Number"
showing 10 items of 3939 documents
On X-saturated formations of finite groups
2005
[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques are also very useful to highlight the properties and behaviour of omega-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.
Learning Molecular Classes from Small Numbers of Positive Examples Using Graph Grammars
2021
We consider the following problem: A researcher identified a small number of molecules with a certain property of interest and now wants to find further molecules sharing this property in a database. This can be described as learning molecular classes from small numbers of positive examples. In this work, we propose a method that is based on learning a graph grammar for the molecular class. We consider the type of graph grammars proposed by Althaus et al. [2], as it can be easily interpreted and allows relatively efficient queries. We identify rules that are frequently encountered in the positive examples and use these to construct a graph grammar. We then classify a molecule as being conta…
Separation conditions on controlled Moran constructions
2017
It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.
Are locally finite MV-algebras a variety?
2021
We answer Mundici's problem number 3 (D. Mundici. Advanced {\L}ukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: (i) The category of locally finite MV-algebras is not equivalent to any finitary variety. (ii) More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. (iii) The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. (iv) The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon th…
Correspondence between some metabelian varieties and left nilpotent varieties
2021
Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of…
Character degrees, character codegrees and nilpotence class of p-groups
2021
Du and Lewis raised in 2016 the question of whether the nilpotence class of a p-group is bounded in terms of the number of character codegrees. In 2020, Croome and Lewis, gave a positive answer to ...
The ideal duplication
2021
AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.
On a conjecture about class numbers of totally positive quadratic forms in totally real algebraic number fields
1979
Zusammenfassung Mittels einer fruheren Klassenzahlabschatzung fur quadratische Formen wird als Verallgemeinerung einer Vermutung von Siegel bewiesen, das Geschlechter totalpositiver Formen mit mindestens drei Variablen und vorgegebener Klassenzahl nur in endlich vielen totalreellen algebraischen Zahlkorpern vorkommen. Bei binaren Formen folgt mit einer neuen Klassenzahlformel aus der verallgemeinerten Riemannschen Vermutung dieselbe Aussage. Ohne Annahme einer Hypothese gilt, das die Anzahl der totalreellen Korper eines festen Grades mit totalpositiven binaren Formen vorgegebener Klassenzahl endlich ist.
Generalized John disks
2014
Abstract We establish the basic properties of the class of generalized simply connected John domains.
Generation of Certain Matrix Groups by Three Involutions, Two of Which Commute
1997
Ž . We say that a group is 2, 2 = 2 -generated if it can be generated by three involutions, two of which commute. The problem of determining Ž . which finite simple groups are 2, 2 = 2 -generated was posed by Mazurov w x in 1980 in the Kourovka notebook 3 . An answer to this problem, for some classes of finite simple groups, was given by Ya. N. Nuzhin, namely for w x Chevalley groups of rank 1 in 4 , for Chevalley groups over a field of w x characteristic 2 in 5 , and for the alternating groups and Chevalley groups w x of type A in 6 . In this paper we consider the problem in the more n general context of matrix groups over arbitrary, finitely generated, commutative rings. As a special case…