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Elements Of Modern Algebra

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 44E: Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union....

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4. Let G be a group and let p be a prime number such that pg = 0 for every element g € G.
a. If G is a commutative group under multiplication, show that the mapping f: G → G given by
f(x)=xP is a homomorphism.
b. If G is an Abelian group under addition, show that the mapping f: G→ G given by f(x) =
xP is a homomorphism.

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