a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...

In this paper, variety means a class of similar algebras—i.e., models of one firstorder language without relation symbols—which is defined by the satisfaction of some fixed sets of equations. A variety is locally finite if all of its finitely generated members are finite. Following J. Berman and P. Idziak [2], the G-spectrum, or generative complexity, of a locally finite variety C, is the funct...

We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...

In this paper we continue our algebraic approach to the study of locally analytic representations of a p-adic Lie group G in vector spaces over a non-Archimedean complete field K. We characterize the smooth representations of Langlands theory which are contained in the new category. More generally, we completely determine the structure of the representations on which the universal enveloping al...

We describe the structure of those locally finite varieties whose first order theory is decidable. A variety is a class of universal algebras defined by a set of equations. Such a class is said to be locally finite if every finitely generated member of the class is finite. It turns out that in order for such a variety to have a decidable theory it must decompose into the varietal product of thr...

In this paper we describe a one–variable Mal′cev–like condition satisfied by any locally finite minimal variety. We prove that a locally finite variety is minimal if and only if it satisfies this Mal′cev–like condition and it is generated by a strictly simple algebra which is nonabelian or has a trivial subalgebra. Our arguments show that the strictly simple generator of a minimal locally finit...

We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension 1 captures precisely the topological cycle space of graphs but works in any di...

In a finite graph, an edge set Z is an element of the cycle space if and only if every vertex has even degree in Z. We extend this basic result to the topological cycle space, which allows infinite circuits, of locally finite graphs. In order to do so, it becomes necessary to attribute a parity to the ends of the graph.

Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].