Groups

Question

If two elements of a group G satisfies $aba^{-1} = b^{2}$ for $b\neq e$ then which of the following is equal to $b^{32}$

$A) a^{16}ba^{-16}$

$B) a^{5}ba^{-5}$

$C) ab^{16}a^{-1}$

$D)$ Both $(B)$ and $(C)$

Comments

D)

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can you explain (B) option and (A)??

i got option(C)

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https://gateoverflow.in/28108/suppose-the-element-a-b-in-a-group-satisfies-aba-1-b2-for-b-e

Answer 1

Similarly expanding using 3 and 4, the answer will be D (B and C both).