# Faye

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9
bio website location age member for 1 year, 10 months seen Feb 25 '13 at 22:41 profile views 51

I am a student who is currently studying at the University of the South Pacific majoring in Mathematics and IS

# 9 Questions

 7 Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups. 2 Let $G$ be a finite group and $H\triangleleft G$ a normal subgroup. Prove that $|G/H| =|G|$ if, and only if, $H = \{e\}$. 2 Give an explicit definition for the different homomorphisms $\psi_1 ,\psi_2:\mathbb{Z}_{5}\to\mathbb{Z}_{5}$. 2 Prove that a group G is not cyclic if, and only if, G is a union of proper subgroups. 1 Prove that if G is an abelian group then the conjugation equivalence relation is the identity relation ($x$ $\thicksim$ $y$ if and only if x=y).

# 97 Reputation

 +15 Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups. +5 Prove that if G is an abelian group then the conjugation equivalence relation is the identity relation ($x$ $\thicksim$ $y$ if and only if x=y). +5 Give an explicit definition for the different homomorphisms $\psi_1 ,\psi_2:\mathbb{Z}_{5}\to\mathbb{Z}_{5}$. +5 Prove that a group G is not cyclic if, and only if, G is a union of proper subgroups.

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# 7 Tags

 0 group-theory × 9 0 equivalence-relations 0 abstract-algebra × 8 0 hopfian-groups 0 abelian-groups × 3 0 permutation-groups 0 cyclic-groups × 2

# 1 Account

 Mathematics 97 rep 9