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This document contains solutions to several problems involving group actions and stabilizer subgroups. Problem A proves that stabilizer subgroups of elements in the same orbit are conjugate subgroups. Problem B shows that the general linear group GL2(R) decomposes into two double cosets of the subgroup of upper triangular matrices. Problem C proves a group acts doubly transitively if and only if it decomposes into two double cosets of a stabilizer subgroup. Problem D shows a fixed point free group action is

Author

Enkhzaya Enkhtaivan

Language

EN