M 型超群的结构与关系

摘要

The notion hypergroup raised by Wall is an important algebraic structure ,it has a great number of im-portant applications in theoretical physics including quantum mechanics and string theory , thus this kind of up-grading of mathematical structure has caused wide concern over the recent years .With the help of this method based on a collection of ideas and promotion , this paper researches the hypergroup based on physical application background , special M-hypergroup with nuclear non-empty, gives the corresponding structure , and proves a se-ries results of M-hypergroup between its subhypergroup and its nuclear .%WALL提出的超群是一种重要的代数结构，在理论物理中的量子力学和超弦理论方面已经取得重要应用，因此数学结构的提升问题引起越来越多人的关注。文章借助这种基于集合提升的思想与方法，研究具有物理应用背景的超群，根据核的非空性得到一类特殊的超群---M型超群，给出了其相应的结构，证明了一系列关于M型超群和其子超群以及与其核关系的结果。