ej Problem 2.8. Let l = pi? p? ... p with the pi distinct primes and the e; non-zero. Let G be an abelian group of order

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Ej Problem 2 8 Let L Pi P P With The Pi Distinct Primes And The E Non Zero Let G Be An Abelian Group Of Order 1 (73.04 KiB) Viewed 17 times

ej Problem 2.8. Let l = pi? p? ... p with the pi distinct primes and the e; non-zero. Let G be an abelian group of order 1. Show that for all i #(K) = pro = Pi and that : K x K2 X ... K*+G, 4((91, 92, ... 9;)) = 9192 ...G; Pi is an isomorphism Hint: induce on j. Get the case j 2 from previous results. For 1 = = pî p 2 ...p;#1: Take n = pi pi? ... p and m = Pj+1 Ke#1 and the group Im = K €1,42 we will decompose by induction. Pi P2 ...P; ej+1 ej €;+1 then In + =