An (H,G)-hypergroup (defined by the author in a preceding paper [Riv. Mat. Univ. Parma (4) 10 (1984), 207--216; MR0865296 (87k:20113)]) is a disjoint union K of sets A_i , where i is taken in a group G and A_1 =H (H is a hypergroup). If two elements x,y are both in H their composition is that of H ; otherwise, if x∈A_i and y∈A_j , let xy=A_ij . The author proves that there exists a bijection between the family of complete subhypergroups of H and the family of subgroups of G , and other properties regarding completeness. Furthermore, he proves that K is regular if and only if H is regular. The paper also contains some results about cyclic (H,G)-hypergroups, morphisms and quotients.

New results on (H,G)-hypergroups

DE SALVO, Mario
1985

Abstract

An (H,G)-hypergroup (defined by the author in a preceding paper [Riv. Mat. Univ. Parma (4) 10 (1984), 207--216; MR0865296 (87k:20113)]) is a disjoint union K of sets A_i , where i is taken in a group G and A_1 =H (H is a hypergroup). If two elements x,y are both in H their composition is that of H ; otherwise, if x∈A_i and y∈A_j , let xy=A_ij . The author proves that there exists a bijection between the family of complete subhypergroups of H and the family of subgroups of G , and other properties regarding completeness. Furthermore, he proves that K is regular if and only if H is regular. The paper also contains some results about cyclic (H,G)-hypergroups, morphisms and quotients.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/2088626
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