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There are no proper morphisms from a given group to C_7

Source: Romanian District Olympiad 2011, Grade XII, Problem 2

October 8, 2018
superior algebramorphismsgroup theory

Problem Statement

Let G G be the set of matrices of the form (ab01), \begin{pmatrix} a&b\\0&1 \end{pmatrix} , with a,b∈Z7,a≠0. a,b\in\mathbb{Z}_7,a\neq 0.
a) Verify that G G is a group. b) Show that Hom((G,⋅);(Z7,+))={0} \text{Hom}\left( (G,\cdot) ; \left( \mathbb{Z}_7,+ \right) \right) =\{ 0\}
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