# Thread:

1. ## subgroup question

Q: Find all possible finite subgroups of the non negative rational numbers under multiplication.

I can only think of the singleton set containing the identity element which would be of order 1. All other sets would be of infinite order. I feel there is more to this though.

thanks

2. Originally Posted by Danneedshelp
Q: Find all possible finite subgroups of the non negative rational numbers under multiplication.

I can only think of the singleton set containing the identity element which would be of order 1. All other sets would be of infinite order. I feel there is more to this though.

thanks

The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

As for your solution it is correct: if $0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft y$ is an infinite set...

Tonio

3. Originally Posted by tonio
The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

As for your solution it is correct: if $0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft y$ is an infinite set...

Tonio
Is it supposed to be $1\ne q\in\mathbb{Q}$ instead of $0<q\in\mathbb{Q}$?

Edit: Meh I was thinking of $\,\mathbb{Q}$ as the positive rationals, should have rewritten the set or instead restricted $q\not\in\{-1,0,1\}$.

4. Originally Posted by tonio
The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

As for your solution it is correct: if $0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft y$ is an infinite set...

Tonio

Oh, my bad. I don't know why I wrote that.

Should it be for all $q\in{\mathbb{Q}}-\{0\}$ and $q\neq\\e$?

Thanks for the help

5. Originally Posted by Danneedshelp
Oh, my bad. I don't know why I wrote that.

Should it be for all $q\in{\mathbb{Q}}-\{0\}$ and $q\neq\\e$?

Thanks for the help

Yes, but it is also true for the positive rationals only (without 1)
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9484294056892395, "perplexity_flag": "middle"}