Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301Grouplikes6585305ENM. H.HooshmandIslamic Azad University - Shiraz BranchJournal Article20090430In this paper we introduce and study an algebraic structure, namely <br />Grouplike. A grouplike is something between semigroup and group and <br />its axioms are generalizations of the four group axioms. <br />Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). <br />The first idea of grouplikes comes from b-parts and $b$-addition <br />of real numbers introduced by the author. Now, the researches have enabled me to <br />introduce Grouplikes and prove some of their main theorems <br />and construct a vast class of them, here. We prove <br />a fundamental structure theorem for a big class of grouplikes, namely <br />Class United Grouplikes. Moreover, we obtain some other results for <br />binary systems, semigroups and groups in general and exhibit several <br />their important subsets with related diagrams. Finally. we show some of future directions <br />for the researches in grouplikes and semigroup theory.http://bims.iranjournals.ir/article_305_daa595cb8449dd1f6b4a0cb354aefa32.pdf