A non-finitely-based variety of center-by-metabelian pointed groups

2014 ◽  
Vol 95 (5-6) ◽  
pp. 743-746
Author(s):  
G. S. Deryabina ◽  
A. N. Krasil’nikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety

A JUST NON-FINITELY BASED VARIETY OF BIGROUPS

2001 ◽  
Vol 29 (9) ◽  
pp. 4011-4046 ◽  
Author(s):  
C. K. Gupta* ◽  
A. N. Krasilnikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety

scholarly journals On the Schur-Baer property

1981 ◽  
Vol 31 (3) ◽  
pp. 343-361 ◽  
Author(s):  
Mohammad Reza R. Moghaddam
Keyword(s):  
Factor Group ◽  
Finitely Based ◽  
Verbal Subgroup ◽  
Finitely Based Variety ◽  
Precise Bound

AbstractIn 1957 P. Hall conjectured that every (finitely based) variety has the property that, for every group G, if the marginal factor-group is finite, then the verbal subgroup is also finite. The content of this paper is to present a precise bound for the order of the verbal subgroup of a G when the marginal factor-group is of order Pn (p a prime and n > 1) with respect to the variety of polynilpotent groups of a given class row. We also construct an example to show that the bound is attained and furthermore, we obtain a bound for the order of the Baer-invariant of a finite p-group with respect to the variety of polynilpotent groups.

scholarly journals On product varieties of groups

1971 ◽  
Vol 5 (2) ◽  
pp. 239-240 ◽  
Author(s):  
M.R. Vaughan-Lee
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety ◽  
Variety Of Groups

An example is given of a finitely based variety of groups such that is not finitely based.Let be the variety of groups determined by the laws (1) [[x1, x2], [x3, x4, [x5, x6]], (2) [[x1, x2, x3], [x4, x5]] [[x1x2], [x4, x5, x3]]−1, [[x1, x2, x3], [x1, x2]]. Then is not finitely based.

A Variety Where the Set of Subalgebras of Finite Simple Algebras is Not Recursive

1998 ◽  
Vol 08 (06) ◽  
pp. 681-688 ◽  
Author(s):  
Stanislav Kublanovsky ◽  
Mark Sapir
Keyword(s):  
Variety Of Algebras ◽  
Finitely Based ◽  
Binary Operations ◽  
Finitely Based Variety ◽  
Simple Algebras

We construct a finitely based variety of algebras with two binary operations where the set of subalgebras of finite simple algebras is not recursive.

FINITELY GENERATED LIMIT VARIETIES OF APERIODIC MONOIDS WITH CENTRAL IDEMPOTENTS

2009 ◽  
Vol 08 (06) ◽  
pp. 779-796 ◽  
Author(s):  
EDMOND W. H. LEE
Keyword(s):  
Present Article ◽  
Variety Of Algebras ◽  
Finitely Based ◽  
Finitely Generated ◽  
Finitely Based Variety ◽  
Limit Variety ◽  
Aperiodic Monoids

A non-finitely based variety of algebras is said to be a limit variety if all its proper subvarieties are finitely based. Recently, Marcel Jackson published two examples of finitely generated limit varieties of aperiodic monoids with central idempotents and questioned whether or not they are unique. The present article answers this question affirmatively.

scholarly journals SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, II.

2003 ◽  
Vol 13 (05) ◽  
pp. 543-564 ◽  
Author(s):  
MARINA SEMENOVA ◽  
FRIEDRICH WEHRUNG
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Convex Sets ◽  
Ordered Set ◽  
Finitely Based ◽  
Locally Finite ◽  
Partially Ordered ◽  
Finitely Based Variety ◽  
Atomistic Lattice ◽  
Convex Subsets

For a positive integer n, we denote by SUB (respectively, SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (respectively, P of length at most n). We prove the following results: (1) SUBn is a finitely based variety, for any n≥1. (2) SUB2 is locally finite. (3) A finite atomistic lattice L without D-cycles belongs to SUB if and only if it belongs to SUB2; this result does not extend to the nonatomistic case. (4) SUBn is not locally finite for n≥3.

Varieties of involution monoids with extreme properties

2019 ◽  
Vol 70 (4) ◽  
pp. 1157-1180
Author(s):  
Edmond W H Lee
Keyword(s):  
The Other ◽  
Sufficient Condition ◽  
Finitely Based ◽  
Finitely Based Variety ◽  
Lattice Of Subvarieties ◽  
Power Set ◽  
Cross Variety ◽  
Positive Integers

Abstract A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties order-embedding the power set lattice of the positive integers. Based on this result, several examples of finite involution monoids with extreme varietal properties are exhibited. These examples—all first of their kinds—include the following: finite involution monoids that generate huge varieties but whose reduct monoids generate Cross varieties; two finite involution monoids sharing a common reduct monoid such that one generates a huge, non-finitely based variety while the other generates a Cross variety; and two finite involution monoids that generate Cross varieties, the join of which is huge.

ON LATTICES EMBEDDABLE INTO LATTICES OF ORDER-CONVEX SETS: CASE OF TREES

2007 ◽  
Vol 17 (08) ◽  
pp. 1667-1712 ◽  
Author(s):  
MARINA V. SEMENOVA ◽  
ANNA ZAMOJSKA-DZIENIO
Keyword(s):  
Convex Sets ◽  
Finitely Based ◽  
Finitely Based Variety

We find a syntactic characterization of the class of lattices embeddable into convexity lattices of posets which are trees. The characterization implies that this class forms a finitely based variety.

scholarly journals Just non-finitely-based varieties of groups

1971 ◽  
Vol 4 (3) ◽  
pp. 343-348 ◽  
Author(s):  
M.F. Newman
Keyword(s):  
Recent Work ◽  
Infinite Number ◽  
Finite Basis ◽  
Finitely Based ◽  
Finitely Based Variety ◽  
Variety Of Groups

A variety of groups is just non-finitely-based if it does not have a finite basis for its laws while all its proper subvarieties do have a finite basis. Recent work of Ol'šanskiiˇ, Vaughan-Lee and Adjan guarantees the existence of at least one just non-finitely-based variety. In this note an infinite number of just non-finitely-based varieties are shown to exist by proving that for every prime p there is a non-finitely based variety of p–groups.

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