A semigroup S is called surjective if S 2 = S. The aim of this paper is to prove that p n-sequences of nite surjective semigroups are eventually strictly increasing, except in few well known cases, when they are bounded. Also, some further types of nite semigroups, obtained by means of subdirect products, are shown to have the same property.

The aim of this paper is to describe the structure finitely generated subgroups a family branch groups, which includes first Grigorchuk group and Gupta-Sidki 3-group. This description made via notion block subgroup. We then use show that all groups in above are subgroup separable (LERF). These results obtained as corollary more general structural statement on subdirect products just infinite gr...

We prove a theorem about subdirect decompositions of lattice effect algebras. Further, we show how, under these decompositions, blocks, sets of sharp elements and centers of those effect algebras are decomposed. As an application we prove a statement about the existence of subadditive state on some block-finite effect algebras.

Infinite cellular automata have been studied mostly using empirical and sta tistical techniques, with some combinatorial analysis. Here we show how concepts of universal algebra such as subdirect decomposition and chains of varieties can be applied to their study. Cellular automata with ultimately periodic behavior are shown to correspond to varieties of groupoids. Relat ionships between these ...