If possible, give two examples of nontrivial proper subgroups of the indicated group. Ifit is not possibe, write IMPOSSIBLE. a) Q, the rational numbers b) Z8 c) D4 d) U(12)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 3E
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Abstract Algebra I
If possible, give two examples of nontrivial proper subgroups of the indicated
group. Ifit is not possibe,write IMPOSSIBLE.
a) Q, the rational numbers
b) Z3
c) D4
d) U(12)
Transcribed Image Text:If possible, give two examples of nontrivial proper subgroups of the indicated group. Ifit is not possibe,write IMPOSSIBLE. a) Q, the rational numbers b) Z3 c) D4 d) U(12)
Du Symme tries of a Square
03
PE
C1234)=P P
(13) (29= pz p2
pt
= p3
Po
12)(34) = =
pt pit
(13) = pE PE
P3
(24)= pre pe
4.
P.
Transcribed Image Text:Du Symme tries of a Square 03 PE C1234)=P P (13) (29= pz p2 pt = p3 Po 12)(34) = = pt pit (13) = pE PE P3 (24)= pre pe 4. P.
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