The set G = {1, 9, 31, 39, 41, 49, 71, 79} is a group under multiplicati modulo 80, with the group table below. 31 39 41 49 71 79 1 9 31 39 41 49 71 79 9 1 39 31 49 41 79 71 elism 8 31 39 1 9 71 79 41 49 9 71 49 41 ildsitusmilib to uoitiatab sul 39 31 9 1 79 41 49 71 79 1 9 31 39 49 41 79 71 9 1 39 31 71 79 41 49 31 39 1 9 79 71 49 41 39 3191 X80 1 9 1 9 31 39 41 49 71 79 Jest noarismo dis tesT of ide hastalog dosa te aldeia od guies piec interval (a) How many elements of order 2 does G have? (b) State a standard group isomorphic to G. (c) Write down all the distinct left cosets of the subgroup N = {1,31} in G. [S] 110 $-a (d) Explain why N is a normal subgroup of G. (e) Write down the group table of the quotient group G/N.
The set G = {1, 9, 31, 39, 41, 49, 71, 79} is a group under multiplicati modulo 80, with the group table below. 31 39 41 49 71 79 1 9 31 39 41 49 71 79 9 1 39 31 49 41 79 71 elism 8 31 39 1 9 71 79 41 49 9 71 49 41 ildsitusmilib to uoitiatab sul 39 31 9 1 79 41 49 71 79 1 9 31 39 49 41 79 71 9 1 39 31 71 79 41 49 31 39 1 9 79 71 49 41 39 3191 X80 1 9 1 9 31 39 41 49 71 79 Jest noarismo dis tesT of ide hastalog dosa te aldeia od guies piec interval (a) How many elements of order 2 does G have? (b) State a standard group isomorphic to G. (c) Write down all the distinct left cosets of the subgroup N = {1,31} in G. [S] 110 $-a (d) Explain why N is a normal subgroup of G. (e) Write down the group table of the quotient group G/N.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The set G = {1, 9, 31, 39, 41, 49, 71, 79) is a group under multiplication
modulo 80, with the group table below.
1
31 39 41 49 71 79
1
9
31 39 41 49 71 79
9 1
39 31 49 41 79 71
elism 8
31 39 1
9
71
79 41 49
39 31 9 1
79
71 49 41 yilliditasi to moitiallob silm
71 49 41
41 49 71 79 1
20-50 =
9 31 39
49 41 79 71 9
1 39 31
71 79 41 49 31 39
19
79 71 49 41 39 31 9 1
X80
1
9
31
39
41
49
71
79
9
Jest noanoqmo ti
test of
bus Statoq oso te oldei
of an interval
Tuismod quis
(SJ) 110$- Sa
(a) How many elements of order 2 does G have?
(b) State a standard group isomorphic to G.
(c) Write down all the distinct left cosets of the subgroup N = {1,31}
in G.
DU
(d) Explain why N is a normal subgroup of G.
(e) Write down the group table of the quotient group G/N.
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