In this paper we shall be mainly concerned with groups which can be covered by (in other words, are unions of) permutable boundedly finite subsets. Obvious examples of such groups are the finite groups, where a single finite set suffices, namely the group itself; and abelian groups, where all one-element subsets will serve. The main result (Theorem 7.1) characterizes these groups completely as ...

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

convergent for \z\ < p, where p > 0, then f(z) is said to have a fixpoint of multiplier ax at 2 = 0. In the (local) iteration of/(?) one studies the sequence {/„(*)},» = 0, 1, 2, • • • in a neighbourhood of z — 0, /n(z) being defined by /oto = * . / « « = / 0 i t o } ^r » = 1 , 2 , 3 , . . . For many values of the multiplier ax, including 0 < \ax\ < 1 and \ax\ > 1, the local iteration of f(z) i...