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Isomorphism types of abelian groups 
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#1
Nov2512, 11:45 AM

P: 41

wrtie down the possible isomorphism types of abelian groups of orders 74 and 800
then for 74=2*37 then Z(74) is isomorphism to Z2 * Z37 (by chinese remainder theorem) then for 74 , 2 we have Z74 and Z2*Z37 (i am not sure it is right or wrong then for 800 i know i should apply the fundamental theorem of fintely generated abelian groups, but i am not quite understand the methods of it , can someone help me the 800 case?????? 


#2
Nov2512, 01:19 PM

P: 772

What does the fundamental theorem say? What have you tried so far?



#3
Nov2512, 06:09 PM

P: 41

so we get 12 different groups: Z25xZ32 Z25xZ16xZ2 Z25xZ8xZ4 Z25xZ4xZ4xZ2 Z25xZ4xZ2xZ2xZ2 Z25xZ2xZ2xZ2xZ2xZ2 Z5xZ5xZ32 Z5xZ5xZ16xZ2 Z5xZ5xZ8xZ4 Z5xZ5xZ4xZ4xZ2 Z5xZ5xZ4xZ2xZ2xZ2 Z5xZ5xZ2xZ2xZ2xZ2xZ2 


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