Show that $Z_5 \times Z_7$ and $Z_{35}$ are isomorphic.

Asked Mar 07 '18 at 19:33

Active Mar 08 '18 at 04:35

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Show that $Z_5 \times Z_7$ and $Z_{35}$ are isomorphic.

I tried $$f(a,b) = 7[a]+ [b]$$

where $a \in Z_5\ and\ b \in Z_7$

Is this Correct ?

** It is similar to this question :

I just read it but can you check if the approach I mentioned to the question is correct ?

edited Mar 08 '18 at 04:35

asked Mar 07 '18 at 19:33

user1611542

Chinese Remainder Theorem? – Angina Seng Mar 07 '18 at 19:34
Can you think of an element of the product that has order $35$? – Ethan Bolker Mar 07 '18 at 19:35
And this question, linked to it. – Dietrich Burde Mar 07 '18 at 19:50
1

@EthanBolker I guess what you are proposing is that Order of (1,1) element in $Z_5 * Z_7$ is 35. hence it is cyclic Group with Order 35. There exists isomorphism between two cyclic groups of same order. Correct ? – user1611542 Mar 08 '18 at 04:30
@LordSharktheUnknown I just read it on wikipedia. It seems the same. – user1611542 Mar 08 '18 at 04:32
@DietrichBurde Thank you for pointing out. Please check the edit. – user1611542 Mar 08 '18 at 04:36

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