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October 3rd, 2009, 06:39 PM  #1 
Newbie Joined: Oct 2009 Posts: 14 Thanks: 0  Subgroup/Normal Subgroup/Factor Group Questions
Let G be the positive reals under multiplication and let H be numbers 2^i where i is in Z. (a) Show H is a subgroup of G. (b) Show H is a Normal subgroup of G. (c) Give a natural representation of the factor group G/H. By this I mean that each element should be uniquely describable as abar where a ranges over some natural set. (So, for example, you couldn’t have 3.1 and 12.4 as 3.1bar = 12.4bar.) Have the identity represented as 1bar. (d) Find all elements abar in G/H whose cube (in G/H) is the identity. (This is a bit tricky. There are precisely three solutions!) 
October 4th, 2009, 03:24 AM  #2  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Subgroup/Normal Subgroup/Factor Group Questions Quote:
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