Let G be a finite abelian group. Then there existsa finite sequence of positive integers (pa¹, p2²,... par)which is unique but for the order of its elements, suchthat p₁, P2,..., pr are primes (not necessarily distinct) anda1, A2,..., a, are positive integers (not necessarily distinct),and G = Z₁ Z... Z..."P₁²

Given : Let G be a finite abelian group.To Prove :Then there exists a finite sequence of positive…

Let G be a finite abelian group. Then there exists a finite sequence of positive integers (pa¹, p2²,... p¹) which is unique but for the order of its elements, such that p1, P2,..., p. are primes (not necessarily distinct) and a1, a2,..., a, are positive integers (not necessarily distinct), and G~ ZZ₂ ... Z eza,. n

Let G be a finite abelian group. Then there exists a finite sequence of positive integers (pa¹, p2²,... p¹) which is unique but for the order of its elements, such that p1, P2,..., p. are primes (not necessarily distinct) and a1, a2,..., a, are positive integers (not necessarily distinct), and G~ ZZ₂ ... Z eza,. n

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 38E: Let n be appositive integer, n1. Prove by induction that the set of transpositions...

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