Does anybody know a general method to find the Group G/H (Where G is a Group and H is a subgroup of G)(adsbygoogle = window.adsbygoogle || []).push({});

For example

(1) What is the group S3/H ?????

S3 = {e, a, a^2, b, ab, (a^2)b} (Permutation group of order 6)

H =< a >= {e, a, a^2} is a cyclic subgroup of G

(2) What is the group GL(n,R)/GL+(n;R)???

GL(n,R) = { nxn Matrices with real entries whose determinants are not zero}

GL+(n;R)= { nxn matrices with real entries whose determiants are positive}

(3) Consider the dihedral group D4 =< a, b >= {e, a, a^2, a^3, b, ab, (a^2)b, (a^3)b}

Find the groups D4/H where H is a normal proper subgroup of D4

(4) Consider S to be the set of all transformations on R such that if x belongs to R

s : x --> x' = ax + b

with a, b real numbers and a not = 0.

Let S1 be all transformations of the form x --> x' = x+b and S2 be all transformations

of the form x --> x' = ax

S/S1 is a group, which group is it?

Help will be greatly appreciated

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# Finding G/H (H Subgroup of G)

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