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INVARIANT RINGS OF FINITE GROUPS OF SMALL ORDER ON THE POLYNOMIAL RING IN TWO VARIABLES

초록/요약

Invariant theory of finite groups is a classical subject of mathematics, which is an important branch of commutative algebra. Classically, the invariant theory have dealt with the question of explicit description of polynomials which do not change under some group actions. In this thesis, by using several theoretical results based on Stanley’s paper, we compute the invariant ring of particular finite groups on the polynomial ring with two variables. Technical methods of calculating the invariant rings are mainly due to those of Sturmfels’ book.

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