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Help!!

cuti3panda
in Linear Algebra and Group Theory

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1)Let G be an Abelian group and let H={g in G/ IgI divides 12}. Prove that H is a subgroup of G. Is there anything special about 12 here? Would your proof be valid if 12 were replaced by some other positive integer? State the general result?

 

2) Find a collection of distint subgroup <a1>, <a2>,.....,<an> of Z240 with the proberty that <a1> C <a2> C.....C <an> with n as large as possible.

 

if you have time, drop me a line anyone!!!

What is the order of xy if x,y are elements of finite abelian group with ord(x)= p and ord(y)=q?

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