'Finite Variety'

2006 ◽  
Vol 35 (1) ◽  
pp. 89-94
Author(s):  
H. Smith
Keyword(s):  
Finite Variety

Semigroup quasivarieties: Two lattices and a reopened problem

2021 ◽  
pp. 1-23
Author(s):  
Tim Koussas
Keyword(s):  
Finite Variety ◽  
Residually Finite ◽  
Partial Correction

We determine all quasivarieties of aperiodic semigroups that are contained in some residually finite variety. This endeavor was initially motivated by a problem in natural dualities, but our work here also serves as a partial correction to an error found in a result of Sapir from the 1980s.

scholarly journals Lattices of pseudovarieties

1989 ◽  
Vol 46 (2) ◽  
pp. 177-183 ◽  
Author(s):  
P. Agliano ◽  
J. B. Nation
Keyword(s):  
Finite Lattice ◽  
Finite Variety ◽  
Locally Finite ◽  
Finite Height ◽  
Lattice Of Subvarieties ◽  
Universal Sentence ◽  
Locally Finite Variety

AbstractWe consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.

scholarly journals The skeleton of a variety of groups

1972 ◽  
Vol 6 (3) ◽  
pp. 357-378 ◽  
Author(s):  
R.M. Bryant ◽  
L.G. Kovács
Keyword(s):  
Free Group ◽  
Finite Groups ◽  
Abelian Groups ◽  
Product Variety ◽  
Finite Variety ◽  
Locally Finite ◽  
Variety Of Groups ◽  
Locally Finite Variety ◽  
Countably Infinite ◽  
Relatively Free Group

The skeleton of a variety of groups is defined to be the intersection of the section closed classes of groups which generate . If m is an integer, m > 1, is the variety of all abelian groups of exponent dividing m, and , is any locally finite variety, it is shown that the skeleton of the product variety is the section closure of the class of finite monolithic groups in . In particular, S) generates . The elements of S are described more explicitly and as a consequence it is shown that S consists of all finite groups in if and only if m is a power of some prime p and the centre of the countably infinite relatively free group of , is a p–group.

Fig. 23 Baffle plate above surface. (From Ref. 29.) portant to avoid air incorporation or foaming), the baffle plate can be lowered to pre-vent splashing. This allows the mixer to be emulsifying at highest speed and, hence, highest shearing rates while avoiding aeration. All mixers or mixing systems must provide flow to all areas of the process ves-sel if they are to be deemed successful. In the case of these axial-flow rotor/stator mixers, the flow emanates from the mixing head and flows in a single direction. In order for the flow to reach every area of the vessel, it must deflect off the baffle plate and then the sidewall. If the mixer cannot produce enough flow to reach the sidewall, then a dead spot exists. The amount of flow required and the amount of flow produced by a given size mixer depends on the viscosity and the design of the specific mixer. The manufacturer should know the pumping capabilities of their mixers at different viscosities in order to select equipment for different size mixing vessels. Table 4 shows the abil-ity of a typical axial-flow rotor/stator mixer. The batch size that can be handled on a macroscale basis can be determined from Table 4 for the axial-flow rotor/stator mixer if the diameter of the process vessel and the diameter of the rotor are known. This is a trial-and-error problem. By choosing a batch size, vessel diameters can be obtained by use of standard-size vessels. If a fea-sible mixer can be installed in a standard-size vessel, the total system capital cost can probably be lowered. The rotor diameters that are available for trial-and-error solution are usually set by the manufacturer. That is, various sizes are available but not an in-finite variety. As an example, take a 1000 gal. process tank with a 72 in. diameter. If a6.5 in. diameter rotor unit is used, a viscosity of up to about 9000 centipoise can be pumped

1998 ◽  
pp. 350-350
Keyword(s):  
Axial Flow ◽  
Capital Cost ◽  
Batch Size ◽  
Total System ◽  
Finite Variety ◽  
Baffle Plate ◽  
Trial And Error ◽  
Standard Size ◽  
Mixing Vessels ◽  
Process Vessel

scholarly journals Jankov Formula and Ternary Deductive Term

10.29007/8fkc ◽  
2018 ◽  
Author(s):  
Alex Citkin
Keyword(s):  
Finite System ◽  
Heyting Algebras ◽  
Finite Variety ◽  
Subdirectly Irreducible ◽  
Locally Finite ◽  
Defining Relations ◽  
Locally Finite Variety ◽  
Canonical Formulas ◽  
Partial Algebras

Grounding on defining relations of a finitely presentable subdirectly irreducible (s.i.) algebra in a variety with a ternary deductive term (TD), we define the characteristic identity of this algebra. For finite s.i. algebras the characteristic identity is equivalent to the identity obtained from Jankov formula. In contrast to Jankov formula, characteristic identity is relative to a variety and even in the varieties of Heyting algebras there are the characteristic identities not related to Jankov formula. Every subvariety of a given locally finite variety with a TD term admits an optimal axiomatization consisting of characteristic identities. There is an algorithm that reduces any finite system of axioms of such a variety to an optimal one. Each variety with a TD term can be axiomatized by characteristic identities of partial algebras, and in certain cases these identities are related to the canonical formulas.

scholarly journals Self-Rectangulating Varieties of Type 5

1997 ◽  
Vol 07 (04) ◽  
pp. 511-540 ◽  
Author(s):  
Keith A. Kearnes ◽  
Ágnes Szendrei
Keyword(s):  
Extension Property ◽  
Congruence Extension Property ◽  
Finite Variety ◽  
Finitely Generated ◽  
Locally Finite ◽  
Term Operation ◽  
Locally Finite Variety ◽  
Definable Principal Congruences

We show that a locally finite variety which omits abelian types is self-rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type-set {5}. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the congruence extension property.

Varieties that make one Cross

1978 ◽  
Vol 26 (3) ◽  
pp. 368-382 ◽  
Author(s):  
Sheila Oates MacDonald ◽  
M. R. Vaughan-Lee
Keyword(s):  
Minimal Condition ◽  
Variety Of Algebras ◽  
Finite Variety ◽  
Associative Algebras ◽  
Maximal Condition ◽  
Locally Finite ◽  
Finite Algebras ◽  
Locally Finite Variety

AbstractAn example is constructed of a locally finite variety of non-associative algebras which satisfies the maximal condition on subvarieties but not the minimal condition. Based on this, counterexamples to various conjectures concerning varieties generated by finite algebras are constructed. The possibility of finding a locally finite variety of algebras which satisfies the minimal condition on subvarieties but not the maximal is also investigated.

scholarly journals Finite potent groups

1981 ◽  
Vol 23 (1) ◽  
pp. 111-120 ◽  
Author(s):  
John Poland
Keyword(s):  
Positive Integer ◽  
Simple Group ◽  
Homomorphic Image ◽  
Nilpotent Groups ◽  
Finite Variety ◽  
Metabelian Groups ◽  
Finite Homomorphic Image

A group is potent if for any element of the group and any prescribed positive integer (dividing its order if this order is finite) there corresponds a finite homomorphic image of the group in which the element has the prescribed integer as its order. The finite potent groups form a finite variety that contains all finite nilpotent groups, all finite metabelian groups, and precisely one simple group, A5.

scholarly journals Finite varieties and groups with Sylow p-subgroups of low class

1981 ◽  
Vol 31 (4) ◽  
pp. 464-469 ◽  
Author(s):  
Rolf Brandl
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Direct Products ◽  
Finite Variety ◽  
Variety Of Groups ◽  
Almost All

AbstractA finite variety is a class of finite groups closed under taking subgroups, factor groups and finite direct products. To each such class there exists a sequence w1, w2,… of words such that the finite group G belongs to the class if and only if wk(G) = 1 for almost all k. As an illustration of the theory we shall present sequences of words for the finite variety of groups whose Sylow p-subgroups have class c for c = 1 and c = 2.

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