Strutures - groups

• May 19th 2013, 02:23 PM
YoungStudent
Strutures - groups
Hy guys .... I hope that are all fine with you ....

I had this exercises to do, and I'm having problems to solving them, can some of you,help me?

**** find the subgroup of the group (Z, +, 0) generated by the set {10, 15} .

best Regards
• May 19th 2013, 05:35 PM
johng
Re: Strutures - groups
Hi,
You posted this same question three different times. Please don't do this. Post your question only once.

What is the subgroup generated by {10,15}? It is the intersection of all subgroups that contain both 10 and 15. Let H={10m +15n : m and n are integers}. You can prove H is a subgroup. Furthermore, any subgroup containing both 10 and 15 must contain each element of H. So H is the subgroup generated by 10 and 15. Now the smallest positive integer in H is 5 (5 = (-1)*10 + 1*15) since one characterization of gcd(10,15) is the smallest positive member of H. Finally, then
H={5n : n is an integer}.
• May 20th 2013, 05:57 AM
YoungStudent
Re: Strutures - groups
Hi there.... sorry for my wrong behavior, posting the same question in different topics.

Thank you for advice and you kindly explanation.