Geodesic
Subgroups of the Power Semigroup of a Finite Semigroup
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1077-1083

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper, S will denote a finite semigroup and Z + the set of positive integers. E = E(S) denotes the set of idempotents of S. Let . If , then let AB = {ab| a ∈ A, b ∈ B}. has been studied by many authors, including [2, 3, 5, 6, 7]. If X is a set, then |X| denotes the cardinality of X. For undefined terms in this paper, see [1,4].THEOREM 1. Let I be an ideal of S, a subgroup of . Then has a normal subgroups such that is isomorphic to a subgroup of and is isomorphic to a subgroup of . 
Putcha, Mohan S. Subgroups of the Power Semigroup of a Finite Semigroup. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1077-1083. doi: 10.4153/CJM-1979-099-1
@article{10_4153_CJM_1979_099_1,
     author = {Putcha, Mohan S.},
     title = {Subgroups of the {Power} {Semigroup} of a {Finite} {Semigroup}},
     journal = {Canadian journal of mathematics},
     pages = {1077--1083},
     year = {1979},
     volume = {31},
     number = {5},
     doi = {10.4153/CJM-1979-099-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-099-1/}
}
TY  - JOUR
AU  - Putcha, Mohan S.
TI  - Subgroups of the Power Semigroup of a Finite Semigroup
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 1077
EP  - 1083
VL  - 31
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-099-1/
DO  - 10.4153/CJM-1979-099-1
ID  - 10_4153_CJM_1979_099_1
ER  - 
%0 Journal Article
%A Putcha, Mohan S.
%T Subgroups of the Power Semigroup of a Finite Semigroup
%J Canadian journal of mathematics
%D 1979
%P 1077-1083
%V 31
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-099-1/
%R 10.4153/CJM-1979-099-1
%F 10_4153_CJM_1979_099_1

[1] 1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Amer. Math. Soc. (Providence, Rhode Island, 1961). Google Scholar

[2] 2. McCarthy, D. J. and Hayes, D. L., Subgroups of the power semigroup of a group, J. of Comb. Theory, ser. A. 14 (1973), 173–186. Google Scholar

[3] 3. Putcha, M. S., On the maximal semilattice decomposition of the power semigroup of a semigroup, Semigroup Foru. 15 (1978), 263–267. Google Scholar

[4] 4. Rhodes, J. L. and Tilson, B. R., Local structure of finite semigroups, in “Algebraic Theory of Machines, Languages, and Semigroups,” M. A. Arbib, éd., Chapter 7 (Academic Press, 1968). Google Scholar

[5] 5. Tamura, T. and Shafer, J., Power semigroups, Math. Japan. 12 (1967), 25–32. Google Scholar

[6] 6. Tamura, T. and Shafer, J., Power semigroups II, Notices AMS, 15 (1968), 395. Google Scholar

[7] 7. Trnkova, V., On a representation of commutative semigroups, Semigroup Foru. 10 (1975), 203–214. Google Scholar

Cité par Sources :