# Abstract Algebra/Manual of Style

This section defines the style rules that should be applied throughout the Abstract Algebra wikibook.

## Purpose

This is intended as a University-level textbook for students of mathematics. Readers are therefore expected to be familiar with math fundamentals, and with the material in the Algebra and Linear Algebra wikibooks.

## Language

The style of the language should be that of an ordinary math textbook: clear and precise but without talking down to the reader. Personal comments should be avoided.

The book should use standard American English spelling throughout.

## Structure

Each page should read like a section of a paper textbook, with external links to further reading where appropriate.(?)

## Chapter and section titles

For top-level chapter titles, all words should be capitalised apart from articles and prepositions (e.g. "Equivalence Relations and Congruence Classes"). Sub-headings within a page should only have the first letter of the heading capitalised.

## Page length restrictions

There are no additional page length restrictions imposed by this style guide, but do follow the global Wikibooks convention of limiting page lengths at 35k (?)

## Templates

With the exception of unimportant comments, each paragraph of text should be preceded with a "type declaration". Common types are Definition, Theorem, Lemma, Example, Note and Remark. A proof should be preceded with the word "Proof" in italics and a semicolon, and ended with a black square: . Code:

{{Unicode|∎}}

The same counter should be used for all types of paragraphs. Example:

Definition 1: ...

Theorem 2: ...

Proof: ...

Remark 3: ...

etc...

Don't link outside the book (except in the introduction to the book as a whole, which can link to other books that are prerequisites).

## Images

All images should be in Wikimedia commons. Since the vast majority of images will be diagrams to illustrate a point in the surrounding text, thumbnails will probably not be appropriate.

## Categories

All book chapters belong under the single category Book:Abstract Algebra

## Notation

Left = first usage, right = last usage

• Groups: ${\displaystyle G}$
• Elements of groups: ${\displaystyle \sigma ,\tau ,\rho }$
• Subgroups: ${\displaystyle H,K,I}$
• Elements of subgroups: ${\displaystyle \eta ,\kappa ,\iota }$
• Normal subgroups: ${\displaystyle N,M}$
• Normal series: ${\displaystyle N_{1},\ldots ,N_{n}}$ , ${\displaystyle M_{1},\ldots ,M_{k}}$
• Generic integers: ${\displaystyle n,k,m,l,j}$
• Summation indices: ${\displaystyle j,k,n}$
• Sequence indices: ${\displaystyle l,m}$