Writing in the Major The assignment is to present a short (4-7 pages) readable and complete account of the semidirect product, and how to use it to produce new groups out of old ones. This topic is covered in section 5.5 in Dummit and Foote, and you should first read and understand that.
(It is also possible to write about another topic, if you have one in mind that you'd like to write about. In that case you must discuss it with me first.)
Target audience You should write your text for someone at a similar stage in a similar class (for example, someone in class who have not yet read this section. Ideally by someone in a similar class using a different textbook). For example, the target audience will already know what a group is, and your paper should not define that.
The emphasis in this assignment is on the exposition (so don't think of this as "solving an exercise", or "finding the solution").
Do: Write whole sentences in proper English. Make sure you define your notation ("Let G be a group and H a subgroup"...). Begin your text with a less technical introduction, with the purpose of giving the reader an idea of what is going to happen in the rest of the paper. Here you could explain what the construction is good foor, why is it interesting, how does it fit into the rest of the mathematics, etc. Proof read! (and maybe ask someone else to proof read too). When you proof read, try to imagine you're someone else who didn't just write the text (can be difficult), and notice which parts which are difficult to comprehend.
Don't: Use abbreviations or unnecessary symbols (you won't need symbols for "for all", "exists", "implies", "therefore").
Deadlines Submit a draft for comments November 9th. Final text due November 28th.