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ArticleOriginal scientific text

Title

Enumeration of Γ-groups of finite order

Authors 1, 1

Affiliations

  1. Faculty of Science, Mahallat institute of higher education, Mahallat, Iran

Abstract

The concept of Γ-semigroups is a generalization of semigroups. In this paper, we consider Γ-groups and prove that every Γ-group is derived from a group then, we give the number of Γ-groups of small order.

Keywords

ENG
Γ-semigroup, Γ-group

Bibliography

  1. E. Alkan, On the enumeration of finite abelian and solvable groups, J. Number Theory 101 (2003) 404-423. doi: 10.1016/s0022-314x(03)00055-6.
  2. S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian J. 26 (2010) 11-23.
  3. A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups (American Mathematical Society, 1967).
  4. A. Cayley, On the theory of groups, as depending on the symbolic equation θⁿ = 1, Phil. Mag. 7 (1854) 40-47.
  5. T.K. Dutta and N.C. Adhikary, On Γ-semigroup with right and left unities, Soochow J. of Math. 19(4) (1993) 461-474.
  6. T.K. Dutta and N.C. Adhikari, On Noetherian Γ-semigroup, Kyungpook Math. J. 36 (1996) 89-95.
  7. P. Erdös, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948) 75-78.
  8. D. Heidari, S.O. Dehkordi and B. Davvaz, Γ-Semihypergroups and their properties, U.P.B. Sci. Bull., Series A 72(1) (2010) 197-210.
  9. D. Heidari and B. Davvaz, Γ-hypergroups and Γ-Semihypergroups associated to binary relations, Iran. J. Sci. Technol. Trans. A Sci. A2 (2011) 69-80.
  10. D. Heidari and M. Amooshahi, Transformation semigroups associated to Γ-semigroups, Discuss. Math. Gen. Algebra Appl. 33(2) (2013) 249-259. doi: 10.7151/dmgaa.1024.
  11. A. Ivić, On the number of abelian groups of a given order and on certain related multiplicative functions, J. Number Theory 16 (1983) 119-137. doi: 10.1016/0022-314x(83)90037-9.
  12. L. Rédei, Das scheife Produkt in der Gruppentheorie, Comment. Math. Helv. 20 (1947) 225-264. doi: 10.1007/bf02568131.
  13. N.K. Saha, On Γ-semigroup II, Bull. Cal. Math. Soc. 79 (1987) 331-335.
  14. M.K. Sen, On Γ-semigroups, in: Proc. of the Int. Conf. on Algebra and it's Appl, Decker Publication (Ed(s)), (New York, 1981).
  15. M.K. Sen and N.K. Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986) 180-186. doi: 10.1090/s0002-9904-1944-080095-6.
  16. A. Seth, Γ-group congruences on regular Γ-semigroups, Internat. J. Math. Math. Sci. (1992) 103-106. doi: 10.1155/so161171292000115.
  17. M. Siripitukdet and A. Iampan, On the Ideal Extensions in Γ-semigroups, Kyungpook Math. J. 48 (2008) 585-591. doi: 10.5666/kmj.2008.48.4.585.
  18. T. Szele, Über die endichen ordnungszahlen, zu denen nur eine gruppe gehört, Comment. Math. Helv. 20 (1947) 265-267. doi: 10.1007/bf02568132.
  19. R. Warlimont, On the set of natural numbers which only yield orders of abelian groups, J. Number Theory 20 (1985) 354-362. doi: 10.1016/0022-314x(85)90026-5.
Discussiones Mathematicae - General Algebra and Applications
2015/35/1
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Pages:
33-39
Main language of publication
English
Received
2014-10-26
Accepted
2015-01-22
Published
2015

DOI: 10.7151/dmgaa.1228

Exact and natural sciences