The assignment is to present a readable and complete discussion 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. The mathematical content of this assignment is not intended to be the primary challenge. The point of this project is to concentrate on the exposition of the topic. Your paper should be 4-7 pages long. The assignment is suggested to be written in latex. Here is a Latex template for the assignment.
Your target audience is a typical Math 120 colleague who has not yet read this section. Your target audience is not me or Daniel. If you have been frustrated by reading mathematical writing in the past (which you undoubtedly have), this is your chance to show how it should be done! In the introduction, you should describe the notion of semidirect product informally, and explain why the reader might want to know about it, and why the notion is important. Put it in some larger context. Give enlightening examples. By the end of the introduction (but not at the start!) there should be a precise definition of the semidirect product. Prepare the reader for what follows by succinctly describing the main ideas and techniques you will use. Then give a detailed dicussion. Be clear what results you are quoting, and try to use as little as possible from earlier in the text. The less self-contained the paper is, the less useful it is to the reader. Do not just say something like "by Theorem 4.2 of the book" --- state any invoked theorem precisely or else give it a descriptive name (such as "the First Isomorphism Theorem"). Your paper should be readable by someone who is familiar with the material of the text up until this section, but who learned it from a different source. You may want a brief conclusion, in which you highlight the key points of the exposition, so your reader can remember them. This is an opportunity to make sure your reader has a big picture in mind. Ask yourself: what should the reader remember after reading this paper? Define your notation ("let G be a group..."). You don't need to define "group", "abelian group", etc.; your target audience is familiar with these notions, and can be assumed to have read everything up until this section of the book. Use complete sentences. Use paragraphs to organize your ideas into logical chunks. Do not use shorthand symbols and words when possible ("iff", right arrows, three dots for therefore, etc.) --- these shorthand symbols are useful for the author, and sometimes necessary during a lecture when time is in short supply, but they needlessly slow down the reader. But definitely use "usual" mathematical notation (of the sort used in the text). Run your draft by someone else (ideally in the class).
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