Find the elementary divisors of the given group a Z250 b Z6

Find the elementary divisors of the given group: (a) Z_250 (b) Z_6 Z_12 Z_18 (c) Z_10 Z_20 Z_30 Z_40 (d) Z_12 Z_30 Z_100 Z_240 Find the invariant factors of each of the groups in Exercise 5.

Solution

a) 250=2*5*5*5

b) 2*2*2*2*3*3*3*3=1296

c) 2*2*2*2*2*2*2*3*5*5*5=2400

	Elementary divisors	Invariant factors
1	Z2×Z5×Z5×Z5	Z10×Z5×Z5
2	Z2×Z5×Z25	Z50×Z5
3	Z2×Z125	Z250