Uno dei metodi migliori per scoprire le proprietà di un cappio chiuso è studiarne il gruppo di moltiplicazione [3], [4]. In questo breve saggio descriviamo i gruppi di moltiplicazione di una classe importante di cappi, e cioè di quella dei cappi flessibili che posseggono la proprietà inversa.
Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which the quasigroups determining the multiplication are linear functions without constant term, called linear abelian extensions. We characterize constructively such extensions with left-, right-, or inverse properties using a general construction according to an...
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We establish...
We prove that the mapping class group and the pure mapping class group of closed non-orientable surfaces with punctures are generated by involutions.
Let be a one-dimensional analytically irreducible ring and let be an integral ideal of . We study the relation between the irreducibility of the ideal in and the irreducibility of the corresponding semigroup ideal . It turns out that if is irreducible, then is irreducible, but the converse does not hold in general. We collect some known results taken from [5], [4], [3] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant decomposition...