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karush

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$\tiny{412.4.2}$

(a) List the elements of the subgroups $\langle 20\rangle $ and $\langle 10\rangle $ in $\Bbb{Z}_{30}$.

(b) Let $a$ be a group element of order 30.

(c) List the elements of the subgroups $\langle a^{20}\rangle $ and $\langle a^{10}\rangle $.

should be easy ... just never did it

(a) $\Bbb{Z}_{30}=(1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)$

$\langle10\rangle = \{0,10,10^2\}= \{0,10,20\}$

$\langle20\rangle = \{0,20,20^2,20^3,20^4...\}$

$20^2 = 20+20 = 10$ so the elements are $\langle20\rangle = \{0,20,10\}$, same as $\langle10\rangle$ .

kinda maybe

(a) List the elements of the subgroups $\langle 20\rangle $ and $\langle 10\rangle $ in $\Bbb{Z}_{30}$.

(b) Let $a$ be a group element of order 30.

(c) List the elements of the subgroups $\langle a^{20}\rangle $ and $\langle a^{10}\rangle $.

should be easy ... just never did it

(a) $\Bbb{Z}_{30}=(1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)$

$\langle10\rangle = \{0,10,10^2\}= \{0,10,20\}$

$\langle20\rangle = \{0,20,20^2,20^3,20^4...\}$

$20^2 = 20+20 = 10$ so the elements are $\langle20\rangle = \{0,20,10\}$, same as $\langle10\rangle$ .

kinda maybe

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