Abstract Algebra- A simple problem with Cosets

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Homework Help Overview

The discussion revolves around finding all the cosets of a given subgroup H in the group Z_16, specifically focusing on the subgroup H={ [0], [4], [8], [12] } and determining the index [Z16 : H].

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the initial steps needed to calculate cosets and the index, with some expressing uncertainty about how to begin. There is a specific inquiry about the appearance of the coset [1]+H.

Discussion Status

The conversation is ongoing, with some participants seeking clarification on foundational concepts while others prompt for details on previous work done. Guidance has been offered regarding the need to show prior efforts in the problem-solving process.

Contextual Notes

Some participants indicate a lack of familiarity with the material, suggesting that they are at an early stage in their understanding of cosets and related concepts.

gipc
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I need to find all the cosets of the subgroup H={ [0], [4], [8] ,[12] } in the group Z_16 and find the index of [Z16 : H].


Help would be appreciated :)
 
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You have to show what work you've done so far. Do you know how to calculate the index at least?
 
I didn't do much work because I'm not sure how to get started on this subject. I've just started this material and I would appreciate if someone showed me how to calculate the coset in a relatively easy question.
 
Do you know what coset [1]+H looks like?
 

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