The group table of a group G of order 10 is given below. e a b C d f g h i j e e a b C d f 9 h i j a agdhje cib f bb dg fci jeah с chfbegidja dd jce hbfagi ffeig bj a c h d ggcji fa hbde hhieda cbjfg i iba jg hd fe C jfhaidegcb (a) Show that G is cyclic and has d as a generator. (b) Find a subgroup of G of order 5. (c) Write down two isomorphisms from the subgroup in part (b) to (Z5, +5).
The group table of a group G of order 10 is given below. e a b C d f g h i j e e a b C d f 9 h i j a agdhje cib f bb dg fci jeah с chfbegidja dd jce hbfagi ffeig bj a c h d ggcji fa hbde hhieda cbjfg i iba jg hd fe C jfhaidegcb (a) Show that G is cyclic and has d as a generator. (b) Find a subgroup of G of order 5. (c) Write down two isomorphisms from the subgroup in part (b) to (Z5, +5).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 5E
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Please give a good amount of detail im enusre how to work out the powers of d. thanks
![The group table of a group G of order 10 is given below.
e
a b
C d f g h i j
e
e
a b C d f 9 h i j
a
agdhje cib f
bb dg fci jeah
с
chfbegidja
dd jce hbfagi
ffeig bj a c h d
ggcji fa hbde
hhieda cbjfg
i iba jg hd fe C
jfhaidegcb
(a)
Show that G is cyclic and has d as a generator.
(b)
Find a subgroup of G of order 5.
(c) Write down two isomorphisms from the subgroup in part (b)
to (Z5, +5).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04fb1644-6128-4051-bfd7-20e522232dc3%2F5b2a24a6-aa41-4335-8963-7eb76c1e48d0%2Floc4ylnc_processed.png&w=3840&q=75)
Transcribed Image Text:The group table of a group G of order 10 is given below.
e
a b
C d f g h i j
e
e
a b C d f 9 h i j
a
agdhje cib f
bb dg fci jeah
с
chfbegidja
dd jce hbfagi
ffeig bj a c h d
ggcji fa hbde
hhieda cbjfg
i iba jg hd fe C
jfhaidegcb
(a)
Show that G is cyclic and has d as a generator.
(b)
Find a subgroup of G of order 5.
(c) Write down two isomorphisms from the subgroup in part (b)
to (Z5, +5).
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