18. An external direct product G₁ G₂ G₂of a finite number of cyclic groups is cyclic if and only if |G₁ and |G₁| are relatively prime when i + j. TRUE FALSE 19. The group ZmZn is cyclic and isomorphic to Zmn if and only if the least common multiple of m and n is 1. TRUE FALSE 20. ZmZn has mn elements whether m and n are relatively prime or not. ● TRUE
18. An external direct product G₁ G₂ G₂of a finite number of cyclic groups is cyclic if and only if |G₁ and |G₁| are relatively prime when i + j. TRUE FALSE 19. The group ZmZn is cyclic and isomorphic to Zmn if and only if the least common multiple of m and n is 1. TRUE FALSE 20. ZmZn has mn elements whether m and n are relatively prime or not. ● TRUE
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer question 18, 19 and 20. Answer if TRUE or FALSE only.
Transcribed Image Text:18. An external direct product G₁ G₂ G₂of a finite number of cyclic groups is cyclic
if and only if |G₁| and |G₁| are relatively prime when i ‡ j.
TRUE
FALSE
19.
The group ZmZn is cyclic and isomorphic to Zmn if and only if the least common
multiple of m and n is 1.
TRUE
FALSE
20.
ZmZn has mn elements whether m and n are relatively prime or not.
●
TRUE
FALSE
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