Generalized topological groups on submaximal spaces

In this paper, we initiate the study of generalized topological groups on submaximal spaces. A generalized topological group has the algebraic structure of groups and the topological structure of a generalized topological space defined by A.csaszar [6] and they are joined together by the requirement that multiplication and inversion areG- continuous. A generalized topological group that if its underlying space is submaximal is called submaximal G-topological groups. The last section is devoted to submaximal G-topological groups, where it is established that each pseudocompact submaximal G- topological group is finite and each totally bounded submaximal G-topological group is countable