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Find all nonisomorphic abelian gps

  • Thread starter mclove
  • Start date
  • #1
5
0

Homework Statement


- List all nonisomorphic abelian groups of order 2^3 3^2 5


Homework Equations





The Attempt at a Solution


- Z_2^3 * Z_3^2 * Z_5 = (iso) Z_360.
Z_2^3 * Z_3 * Z_3 * Z_5 = (iso) Z_3 * Z_100
.
.
.
I know ,
but why Z_360 , Z_3 * Z_100 are nonisomorphic to 2^3 3^2 5 ?
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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Because Z_360 == Z_2^3 * Z_3^2 * Z_5, but Z_3 * Z_100 == Z_2^3 * Z_3 * Z_3 * Z_5.
 
  • #3
5
0
Sorry, I don's understand it..
Z_2^3 * Z_3 * Z_3* Z_5 == Z_8 * Z_9 * Z_5 Is this nonabelian groups of order
2^33^25 ??
 

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