Journal
DISCRETE MATHEMATICS
Volume 307, Issue 22, Pages 2826-2836Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.disc.2007.03.001
Keywords
type U hypergroups; semihypergroups; cyclic semihypergroups; D-hypergroups
Categories
Ask authors/readers for more resources
We generalize the classical definition of hypergroups of type U on the right to semihypergroups, and we prove some properties of their subsemihypergroups and subhypergroups. In particular, we obtain that a finite proper semihypergroup of type U on the right can exist only if its order is at least 6. We prove that one such semihypergroup of order 6 actually exists. Moreover, we show that there exists a hypergroup of type U on the right of cardinality 9 containing a proper non-trivial subsemihypergroup. In this way, we solve a problem left open in [D. Freni, Sur les hypergroupes de type U et sous-hypergroupes engendres par un sous-ensemble, Riv. Mat. Univ. Parma 13 (1987) 29-41]. (C) 2007 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available