The Penetration and Application of Group Theory Thought in Algebraic Combinatatorics

Algebraic combinatorics, as a cross subject between combinatorics and abstract algebra, is regarded as “group theory without the group” in the international mathematics world. In this paper some representative problems in algebraic combinatorics, such as association schemes, primitive association schemes, Sylow theorems, character theory and duality are selected for analysis from the perspective of structural mathematics. The penetration and application of the theory and methods of group theory to algebraic combinatorics are explained. By finding the common logic basis, common concept basis and common method basis of algebraic combinatorics and group theory, the important position and promoting role of group theory in the history of algebraic combinatorics is presented.