(a) A group of order 142020 containing a subgroup of order 7.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 32E: 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping ...
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Questions in the attached image, thank you in advance.
![(a) A group of order 142020 containing a subgroup of order 7.
(b) A group G acting on a set X, such that there exists x € X for which the stabilizer G is not a
normal subgroup of G.
(c) A ring homomorphism 4: R[x, y] → Z[z] with y(R[x, y]) ‡ {0} whose kernel is not a prime
ideal (x, y, z are independent variables).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42044228-cff6-4391-9596-005bad4f5c7f%2Fafd8e68d-d86d-4143-9131-249e61c59490%2Feb3em79_processed.png&w=3840&q=75)
Transcribed Image Text:(a) A group of order 142020 containing a subgroup of order 7.
(b) A group G acting on a set X, such that there exists x € X for which the stabilizer G is not a
normal subgroup of G.
(c) A ring homomorphism 4: R[x, y] → Z[z] with y(R[x, y]) ‡ {0} whose kernel is not a prime
ideal (x, y, z are independent variables).
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