scholarly journals On the endomorphism near-ring of a free group

1980 ◽  
Vol 23 (1) ◽  
pp. 103-121 ◽  
Author(s):  
R. Warwick Zeamer
Keyword(s):  
Wreath Product ◽  
Free Group ◽  
The Other ◽  
Finite Support ◽  
Finite Product ◽  
Prime Factorization ◽  
Infinite Rank ◽  
One To One ◽  
Almost All ◽  
Countably Infinite

Suppose F is an additively written free group of countably infinite rank with basis T and let E = End(F). If we add endomorphisms pointwise on T and multiply them by map composition, E becomes a near-ring. In her paper “On Varieties of Groups and their Associated Near Rings” Hanna Neumann studied the sub-near-ring of E consisting of the endomorphisms of F of finite support, that is, those endomorphisms taking almost all of the elements of T to zero. She called this near-ring Φω. Now it happens that the ideals of Φω are in one to one correspondence with varieties of groups. Moreover this correspondence is a monoid isomorphism where the ideals of φω are multiplied pointwise. The aim of Neumann's paper was to use this isomorphism to show that any variety can be written uniquely as a finite product of primes, and it was in this near-ring theoretic context that this problem was first raised. She succeeded in showing that the left cancellation law holds for varieties (namely, U(V) = U′(V) implies U = U′) and that any variety can be written as a finite product of primes. The other cancellation law proved intractable. Later, unique prime factorization of varieties was proved by Neumann, Neumann and Neumann, in (7). A concise proof using these same wreath product techniques was also given in H. Neumann's book (6). These proofs, however, bear no relation to the original near-ring theoretic statement of the problem.

scholarly journals A solution of a problem of Plotkin and Vovsi and an application to varieties of groups

1999 ◽  
Vol 67 (3) ◽  
pp. 329-355 ◽  
Author(s):  
C. K. Gupta ◽  
A. N. Krasil'nikov
Keyword(s):  
Free Group ◽  
Invariant Subgroup ◽  
Arbitrary Field ◽  
Finitely Based ◽  
Maximal Condition ◽  
Infinite Rank ◽  
Characteristic 2 ◽  
Countably Infinite ◽  
Fully Invariant Subgroups ◽  
Relatively Free Group

AbstractLet K be an arbitrary field of characteristic 2, F a free group of countably infinite rank. We construct a finitely generated fully invariant subgroup U in F such that the relatively free group F/U satisfies the maximal condition on fully invariant subgroups but the group algebra K (F/U) does not satisfy the maximal condition on fully invariant ideals. This solves a problem posed by Plotkin and Vovsi. Using the developed techniques we also construct the first example of a non-finitely based (nilpotent of class 2)-by-(nilpotent of class 2) variety whose Abelian-by-(nilpotent of class at most 2) groups form a hereditarily finitely based subvariety.

scholarly journals When endomorphisms of G inducing automorphisms of G/V are automorphisms

1987 ◽  
Vol 30 (1) ◽  
pp. 115-120
Author(s):  
O. Macedońska
Keyword(s):  
Free Group ◽  
Commutator Subgroup ◽  
Vector Representation ◽  
Verbal Subgroup ◽  
Infinite Rank ◽  
Fixed Set ◽  
Free Generators ◽  
Countably Infinite ◽  
Relatively Free Group

Let G denote a relatively free group of a finite or countably infinite rank with a fixed set of free generators x1,x2,…,G′ the commutator subgroup, and V a verbal subgroup belonging to G′. Following H. Neumann [6] we shall use the vector representation for endomorphisms of G. Vector v = (ν1, ν2,…) represents an endomorphism v such that xiv = νi for all i. The identity map is represented by l=(x1,x2…). We need also thetrivial endomorphism 0 = (e, e,…). The length of vectors is equal to the rank of G. We shall consider the near-ring of vectors, with addition and multiplication given below u + v=(ulν1, u2ν2,…) where uiνi; is a product in G, and uv = (u1v, u2v,…) where uiv isthe image of ui, under the endomorphism v. There is only one distributivity law (u + v)w =uw + vw.

scholarly journals Generating groups of certain soluble varieties

1974 ◽  
Vol 17 (2) ◽  
pp. 222-233 ◽  
Author(s):  
Narain Gupta ◽  
Frank Levin
Keyword(s):  
Free Group ◽  
Finite Rank ◽  
Free Groups ◽  
Infinite Rank ◽  
Variety Of Groups ◽  
Countably Infinite

Any variety of groups is generated by its free group of countably infinite rank. A problem that appears in various forms in Hanna Neumann's book [7] (see, for intance, sections 2.4, 2.5, 3.5, 3.6) is that of determining if a given variety B can be generated by Fk(B), one of its free groups of finite rank; and if so, if Fn(B) is residually a k-generator group for all n ≧ k. (Here, as in the sequel, all unexplained notation follows [7].)

scholarly journals All automorphisms of the 3-nilpotent free group of countably infinite rank can be lifted

1988 ◽  
Vol 118 (1) ◽  
pp. 120-128 ◽  
Author(s):  
Piotr Włodzimierz Gawron ◽  
Olga Macedońska
Keyword(s):  
Free Group ◽  
Infinite Rank ◽  
Countably Infinite

Starość w nauczaniu św. Bazylego Wielkiego

Vox Patrum ◽  
2011 ◽  
Vol 56 ◽  
pp. 339-348
Author(s):  
Bogdan Czyżewski
Keyword(s):  
Old Age ◽  
Spiritual Maturity ◽  
The Other ◽  
Interesting Aspect ◽  
Other Hand ◽  
Physical Suffering ◽  
Way Of Thinking ◽  
Almost All

Although St. Basil did not live 50 years, the topic of the old age appears in his works quite often. On the other hand, it is clear that Basil does not discuss this issue in one par­ticular work or in the longer argumentation. The fragmentary statements about old age can be found in almost all his works, but most of them can be found in the correspondence of Basil. In this paper we present the most important ad the most interesting aspect of teach­ing of Basil the Great. As these certificates show that the bishop of Caesarea looked at the old age maturely, rationally estimated passage of time, which very often makes a man different. He experienced it, for example as a spiritual and physical suffering, which often were connected with his person. He saw a lot of aspect of the old age, especially its advan­tages – spiritual maturity and wisdom. What is more, he pointed also to passage of time, which leads a man to eternity, which should be prepared to, regardless how old he is. In his opinion fear is not seen opinions of St. Basil present really Christian way of thinking, well-balanced and calm.

Development of a Single-Code/Default Coding Strategy in Pigeons

2000 ◽  
Vol 11 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Tricia S. Clement ◽  
Thomas R. Zentall
Keyword(s):  
Conditional Discrimination ◽  
The Other ◽  
Matching Accuracy ◽  
Efficient Coding ◽  
Coding Strategy ◽  
One To One ◽  
Retention Intervals ◽  
The Many ◽  
The One ◽  
Better Than

We tested the hypothesis that pigeons could use a cognitively efficient coding strategy by training them on a conditional discrimination (delayed symbolic matching) in which one alternative was correct following the presentation of one sample (one-to-one), whereas the other alternative was correct following the presentation of any one of four other samples (many-to-one). When retention intervals of different durations were inserted between the offset of the sample and the onset of the choice stimuli, divergent retention functions were found. With increasing retention interval, matching accuracy on trials involving any of the many-to-one samples was increasingly better than matching accuracy on trials involving the one-to-one sample. Furthermore, following this test, pigeons treated a novel sample as if it had been one of the many-to-one samples. The data suggest that rather than learning each of the five sample-comparison associations independently, the pigeons developed a cognitively efficient single-code/default coding strategy.

Descriptions of the larvae of four species of Procladius from Great Slave Lake (Chironomidae:Diptera)

1978 ◽  
Vol 56 (9) ◽  
pp. 2055-2057 ◽  
Author(s):  
J. W. Moore ◽  
I. A. Moore
Keyword(s):  
Antennal Segment ◽  
The Other ◽  
Large Size ◽  
Great Slave Lake ◽  
Palpal Segment ◽  
Almost All

Descriptions of larvae of Procladius denticulatus, Procladius culiciformis, Procladius freemani, and Procladius bellus collected from Yellowknife Bay (lat., 62°25′; long., 114°20′) are given. Procladius denticulatus was separated from the other species by its large size, a character which always proved distinctive. Procladius culiciformis and P. freemani were separated from one another through several measurements including those of the basal antennal segment and the basal palpal segment. Almost all characters of the head were useful in distinguishing the much smaller P. bellus from the other species.

scholarly journals Geographical matching of volatile signals and pollinator olfactory responses in a cycad brood-site mutualism

2015 ◽  
Vol 282 (1816) ◽  
pp. 20152053 ◽  
Author(s):  
Terence N. Suinyuy ◽  
John S. Donaldson ◽  
Steven D. Johnson
Keyword(s):  
Choice Experiments ◽  
Local Region ◽  
The Other ◽  
Beetle Species ◽  
Olfactory Preference ◽  
Olfactory Responses ◽  
Volatile Emissions ◽  
Extant Species ◽  
Insect Pollinators ◽  
Almost All

Brood-site mutualisms represent extreme levels of reciprocal specialization between plants and insect pollinators, raising questions about whether these mutualisms are mediated by volatile signals and whether these signals and insect responses to them covary geographically in a manner expected from coevolution. Cycads are an ancient plant lineage in which almost all extant species are pollinated through brood-site mutualisms with insects. We investigated whether volatile emissions and insect olfactory responses are matched across the distribution range of the African cycad Encephalartos villosus . This cycad species is pollinated by the same beetle species across its distribution, but cone volatile emissions are dominated by alkenes in northern populations, and by monoterpenes and a pyrazine compound in southern populations. In reciprocal choice experiments, insects chose the scent of cones from the local region over that of cones from the other region. Antennae of beetles from northern populations responded mainly to alkenes, while those of beetles from southern populations responded mainly to pyrazine. In bioassay experiments, beetles were most strongly attracted to alkenes in northern populations and to the pyrazine compound in southern populations. Geographical matching of cone volatiles and pollinator olfactory preference is consistent with coevolution in this specialized mutualism.

Anna Karenina: The Dialectic of Prophecy

PMLA ◽  
1964 ◽  
Vol 79 (3) ◽  
pp. 266-282
Author(s):  
David H. Stewart
Keyword(s):  
Nineteenth Century ◽  
The Other ◽  
Moby Dick ◽  
Anna Karenina ◽  
Symbolic Value ◽  
Almost All ◽  
The Way

One of the most impressive features of Anna Karenina is the way in which Tolstoy draws the reader's imagination beyond the literal level of the narrative into generalizations that seem mythical in a manner difficult to articulate. With Dostoevsky or Melville, one sees immediately a propensity for exploiting the symbolic value of things. With Tolstoy, things try, as it were, to resist conversion: they strive to maintain their “thingness” as empirical entities. A character in Dostoevsky is usually only half man; the other half is Christ or Satan. Moby Dick is obviously only half whale; the other half is Evil or some principle of Nature. But Anna Karenina is emphatically Anna Karenina. Like almost all of Tolstoy's characters, she has a proficiency in the husbandry of identity; she jealously hoards her own unique reality, so that it becomes difficult to say of her that she is a “type” of nineteenth-century Russian lady or a “symbol” of modern woman or an “archetypical” Eve or Lilith.

Sign in / Sign up

Export Citation Format

Share Document