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January 9th, 2016, 09:28 AM  #1 
Newbie Joined: Jan 2016 From: Delhi Posts: 2 Thanks: 0  Finding the order of a quotient group.
Let G be a group of 2×2 matrix with integer entries (under matrix addition) and let H be the subgroup of G consisting of matrices with even entries . Then how to find the order of the quotient group G/H ?

January 9th, 2016, 12:25 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Do you know the meanings of the words you are using here? In particular do you know how the "quotient group" of defined? Look at a simpler version: suppose G is the group of all integers with ordinary addition as the operation, H is the subgroup of even integers. What things are in G/H? What are the cosets of G with respect to H? (Do you know what that means?)

January 9th, 2016, 05:14 PM  #3 
Newbie Joined: Jan 2016 From: Delhi Posts: 2 Thanks: 0 
Yes, the words used here are all known to me. I have not mentioned one thing in my post is that H is normal subgroup of G. But I thought that the index of H in G i.e. [G:H] will be equal to 2 so it will be normal (if I am not wrong) which is required for G/H to be a quotient group. Z/2Z = { x+2Z : x is in Z } will be the required set for your question. Actually my problem here is because of the word matrix. Because I have seldom used this kind of quotient group. My question is how to attack such questions, at least how to think over such questions? With regards. Thank you. 

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