# Identify The Quotient Group

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Is a group where. 2. 2. and . H xH. xH. H x H x H. = = . Question: 5. Identify the quotient group / P. where P denotes the subgroup of positive real numbers. Answer: / P. is a group since is abelian. Two real numbers a, b are in the same cosets if and only if. 1 ab. P. why? . Thus 2 real numbers 0 . .. - Let 's look at a slightly more "in-depth" example: Consider the subgroup 7 Z of Z which consists of all positive, negative and 0 multiples of 7 . Let 's "expand" this a bit: 7 Z = { , 21 , 14 , 7 , 0 , 7 , 14 , 21 , 28 , } What set do we get if we add 1 to everything in this set? 1 + 7 Z = { , 20 , 13 , 6 , 1 . - @GerryMyerson : I do not understand your idea :O could you please explain a bit more - user ':55. @TattwamasiAmrutam : why do you think the quotient group is same as what you have written it would be better if you can try writing that partially - user ':57..

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• ### Abstract Alge Identifying A Quotient Group Nbhm

Let \$\mathbb C^*\$ denote the multiplicative group of non-zero complex numbers and let \$P\$ denote the subgroup of positive real numbers. Identify the quotient group..

• ### Quotient Group Wikipedia

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that .

• ### Identify Quotient Group Mathematics Stack Exchange

Identify quotient group R/R+ where R is multiplicative group of non zero reals and R+ denotes subgroup of positive real numbers. I'm using first isomorphism theorem. We will define a map which is on tomorphism and its kernel will be R+..

• ### Identifying Quotient Groups Math Help Forum

Identifying Quotient Groupso, Given the set G of invertible, upper triangular 2x2 matrices, it can be verified that G forms a subgroup of the general linear group invertible matrices of 2x2 matrices with real entries..

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