abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

Abstract. Let (R,P) be a Noetherian unique factorization do-main (UFD) and M be a finitely generated R-module. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphi...

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Let G be a finite group. A collection $$\Pi =\{H_1,\dots ,{H_r}\}$$ of subgroups G, where $$r>1$$ , is said non-trivial partition if every non-identity element belongs to one and only $$H_i$$ for some $$1\leqslant i\leqslant r$$ . We call group that does not admit any partition-free In this paper, we study whose all proper non-cyclic partitions.

In previous work, the first author established a natural bijection between minimal subshifts and maximal regular J -classes of free profinite semigroups. In this paper, the Schützenberger groups of such J -classes are investigated, in particular in respect to a conjecture proposed by the first author concerning their profinite presentation. The conjecture is established for all non-periodic min...