Sabri  Sadiku, 
    Necessary and Sufficient Conditions Where One Γ-Semigroup is a Γ-Group,
    Journal of Modern Mathematics and Statistics,
    Volume 4,Issue 1,
    2010,
    Pages 44-49,
    ISSN 1994-5388,
    jmmstat.2010.44.49,
    (https://makhillpublications.co/view-article.php?doi=jmmstat.2010.44.49)
    Abstract: In this study, researchers have studied the Γ-algebraic structures and some characteristics of them. According to Sen and Saha, we defined algebraic structures: Γ-semigroup, Γ-regular semigroup, Γ-idempotent semigroup, Γ-invers semigroup and Γ-group. Theorem 2, 3 and 4 proves the existence of Γ-group and gives necessary and sufficient conditions where one Γ-semigroup is a Γ-group. Finally, theorem 5 shows necessary and sufficient conditions where one Γ-regular semigroup is a Γ-group. In addition, for every Γ- algebraic structure that we mentioned before we give an original example.
    Keywords: ±-idempotent element;(±; ²)-inverse element;“-semigroups;“-algebraic structures;“-semigroup idempotent;“-group