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- Feb 15, 2012

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You are given a group as a quotient of the free group on two letters, a and b.

the kernel of the surjective homomorphism $F_2 \to G$ is generated by:

$\{a^7,b^6,a^4ba^{-1}b^{-1}\}$

a) prove $G$ is solvable by identifying the derived series:

$G' = [G,G] > G^{\prime \prime} = [G',G'] > \dots $

b) determine the isomorphism class of $G$

(hint: you have 6 to choose from)

the kernel of the surjective homomorphism $F_2 \to G$ is generated by:

$\{a^7,b^6,a^4ba^{-1}b^{-1}\}$

a) prove $G$ is solvable by identifying the derived series:

$G' = [G,G] > G^{\prime \prime} = [G',G'] > \dots $

b) determine the isomorphism class of $G$

(hint: you have 6 to choose from)

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