let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

Let G be an uncountable universal locally finite group. We study subgroups H < G such that for every g ∈ G, |H : H ∩H| < |H|.

DEFINITION. A group G is called a universal locally finite central extension of A provided that the following conditions are satisfied. (i) A <= (G (the centre of G). (ii) G is locally finite. (iii) (/1-injectivity). Suppose that A <= B <= D with A a (D, that D/A is finite, and that q>: B -> G is an ^-isomorphism (that is, q>{a) = a for all as A). Then there exists an extension q>: D -*• G of (...

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].