Vol. 111, No. 2, 1984

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Hypergroup joins and their dual objects

Richard Vrem

Vol. 111 (1984), No. 2, 483–495

A hypergroup join is a hypergroup formed by the union of a discrete hypergroup with a compact hypergroup. The compact hypergroup is a subhypergroup of the join, but the convolution on the discrete hypergroup is changed in the join. A characterization of compact joins in terms of their dual objects is given which leads to a simpler criteria for their existence. In particular, it is shown that if a compact abelian join has a dual which is a hypergroup, then the dual is also a join. Examples of joins are provided from the study of conjugacy classes of certain semi-direct products of compact groups and a method is described for constructing non-dualizable compact abelian hypergroups.

Mathematical Subject Classification 2000
Primary: 43A10
Secondary: 22A30
Received: 26 April 1982
Revised: 29 July 1982
Published: 1 April 1984
Richard Vrem