Enumeration of Γ-groups of finite order

Dariush Heidari; Marzieh Amooshahi

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 1, page 33-39
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Dariush Heidari, and Marzieh Amooshahi. "Enumeration of Γ-groups of finite order." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 33-39. <http://eudml.org/doc/270288>.

@article{DariushHeidari2015,
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.},
author = {Dariush Heidari, Marzieh Amooshahi},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Γ-semigroup; Γ-group},
language = {eng},
number = {1},
pages = {33-39},
title = {Enumeration of Γ-groups of finite order},
url = {http://eudml.org/doc/270288},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Dariush Heidari
AU - Marzieh Amooshahi
TI - Enumeration of Γ-groups of finite order
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 1
SP - 33
EP - 39
AB - 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.
LA - eng
KW - Γ-semigroup; Γ-group
UR - http://eudml.org/doc/270288
ER -

References

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  1. [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. Zbl1038.11064
  2. [2] S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian J. 26 (2010) 11-23. Zbl1197.20061
  3. [3] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups (American Mathematical Society, 1967). Zbl0178.01203
  4. [4] A. Cayley, On the theory of groups, as depending on the symbolic equation θⁿ = 1, Phil. Mag. 7 (1854) 40-47. 
  5. [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. Zbl0802.20053
  6. [6] T.K. Dutta and N.C. Adhikari, On Noetherian Γ-semigroup, Kyungpook Math. J. 36 (1996) 89-95. Zbl0872.20055
  7. [7] P. Erdös, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948) 75-78. Zbl0041.36807
  8. [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. Zbl1197.20062
  9. [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. [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. Zbl1301.20066
  11. [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. [12] L. Rédei, Das scheife Produkt in der Gruppentheorie, Comment. Math. Helv. 20 (1947) 225-264. doi: 10.1007/bf02568131. Zbl0035.01503
  13. [13] N.K. Saha, On Γ-semigroup II, Bull. Cal. Math. Soc. 79 (1987) 331-335. 
  14. [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. [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. [16] A. Seth, Γ-group congruences on regular Γ-semigroups, Internat. J. Math. Math. Sci. (1992) 103-106. doi: 10.1155/so161171292000115. Zbl0746.20051
  17. [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. [18] T. Szele, Über die endichen ordnungszahlen, zu denen nur eine gruppe gehört, Comment. Math. Helv. 20 (1947) 265-267. doi: 10.1007/bf02568132. Zbl0034.30502
  19. [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. Zbl0576.10031

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