Full Text:
<2383>
CLC number: 20N20
On-line Access:
Received: 2001-09-15
Revision Accepted: 2002-12-11
Crosschecked: 0000-00-00
Cited: 1
Clicked: 4090
Construction of some hypergroups from combinatorial structures
| |||||||||||||
Ali Reza Ashrafi, Ahmad Reza Eslami-Harandi. Construction of some hypergroups from combinatorial structures[J]. Journal of Zhejiang University Science A, 2003, 4(1): 76-79.
@article{title="Construction of some hypergroups from combinatorial structures",
author="Ali Reza Ashrafi, Ahmad Reza Eslami-Harandi",
journal="Journal of Zhejiang University Science A",
volume="4",
number="1",
pages="76-79",
year="2003",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2003.0076"
}
%0 Journal Article
%T Construction of some hypergroups from combinatorial structures
%A Ali Reza Ashrafi
%A Ahmad Reza Eslami-Harandi
%J Journal of Zhejiang University SCIENCE A
%V 4
%N 1
%P 76-79
%@ 1869-1951
%D 2003
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2003.0076
TY - JOUR
T1 - Construction of some hypergroups from combinatorial structures
A1 - Ali Reza Ashrafi
A1 - Ahmad Reza Eslami-Harandi
J0 - Journal of Zhejiang University Science A
VL - 4
IS - 1
SP - 76
EP - 79
%@ 1869-1951
Y1 - 2003
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2003.0076
Abstract: Jajcay's studies (1993; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Syme(G), the stabilizer of the identity e∈G in the group Sym(G). We prove that (Syme(G), ⊙) is a hypergroup and characterize the subhypergroups of this hypergroup. Finally, we show that the set of all subhypergroups of Syme(G) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut(G).
[1]Biggs, N.and White,A.T., 1979. Permutation Groups and Combinatorial Structures. Mathematical Society Lecture Notes 33, Cambridge University Press, Cambridge.
[2]Birkhoff,G., 1967. Lattice Theory(3rd. ed.), AMS Coll. Publ.Providence.
[3]Corsini,P., 1993, Prolegomena of Hypergroup Theory. Second Edition, Aviani Edittore.
[4]Jajcay,R., 1993, Automorphism groups of Cayley maps. J. of Comb. Theory, Ser.B, 59: 297-310.
[5]Jajcay, R., 1994, On a new product of groups. Europ. J. Combinatorics, 15: 251-252.
[6]Madanshekaf,A. and Ashrafi,A.R., 1998. Generalized Action of a hypergroup on a set. Italian J. of Pure and Appl. Math., (3): 127-135.
[7]Marty,F., 1934.Sur une generalization de lanotion de groupe, 8iem Congress Math. Scandinaves, Stockholm. p.45-49.
[8]Vougiouklis,T., 1994. Hyperstructures and their Representations, Hadronic Press, Inc.
Open peer comments: Debate/Discuss/Question/Opinion
<1>