- 19,944
- 11,035
What is the smallest positive integer n such that there are exactly 3 nonisomorphic Abelian group of order n
Challenge 25: Finite Abelian Groups
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
6 replies · 1K views
- 2,802
- 605
Its 8!
- 19,944
- 11,035
Show your work! :)Shyan said:
Last edited:
- 2,802
- 605
I thought its legitimate to use our searching skills!:DGreg Bernhardt said:
- 37,487
- 14,377
n cannot be square-free (it needs factors that are multiples of each other), otherwise you don't get multiple non-isomorphic groups. The first two numbers with that property are 4 (leading to 2 different groups, corresponding to "4" and "2x2") and 8 ("8", "4x2", "2x2x2"). Therefore, 8 is the smallest n.
DarthMatter
- 94
- 10
Shyan said:
Oh come on!
If that's not a big spoiler, I don't know what is.
Joffan
- 473
- 13
Haha, I misread the challenge as asking for 3 non-Abelian groups, so - also using searching skills - I came to a different answer.