Finite and cyclic colombian group
Source: IberoAmerican Olympiad For University Students
July 10, 2011
group theoryabstract algebraRing Theorysuperior algebrasuperior algebra unsolved
Problem Statement
Let be a field whose characteristic is not , let be its multiplicative group and let be the subgroup of constituted by its finite order elements. Prove that if is finite, then is cyclic and its order is even.