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a) Prove that, the characteristic of an integral domain R is either zero or a prime number. b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is cyclic.

a) Prove that, the characteristic of an integral domain R is either zero or a prime number. b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is cyclic.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 29E: Let be a group of order , where and are distinct prime integers. If has only one subgroup of...
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a) Prove that, the characteristic of an integral domain R is either zero or a prime number. b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is cyclic.
Transcribed Image Text:a) Prove that, the characteristic of an integral domain R is either zero or a prime number. b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is cyclic.
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