# Course - Groups and Group Actions HT23

> Source: https://ollybritton.com/notes/uni/prelims/ht23/groups/ · Updated: 2025-09-30 · Tags: uni, course

> This course introduced the idea of a group, which is a fundamental mathematical structure that can be thought of as the way of encoding all of the symmetries of something. It's also the first time seeing the idea of a quotient, which shows up in lots of other courses. This means you can give precise meaning to statements like "the complex numbers without ('mod') the real numbers are just angles" ($\mathbb C / \mathbb R \cong S^1$).

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=617)
- [Lecture Notes](https://courses.maths.ox.ac.uk/pluginfile.php/25607/mod_resource/content/1/Richard_Earl_lectures.pdf)
- Predecessor to: [Course - Groups and Group Actions TT23](https://ollybritton.com/notes/uni/prelims/tt23/groups/)
- Other courses this term: [Courses HT22](https://ollybritton.com/notes/uni/prelims/ht23/)
- Related books:
	- [The Fascination of Groups](https://ollybritton.com/notes/books/the-fascination-of-groups/)

### Notes
- [Notes - Groups HT23, Group axioms](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/group-axioms/)
- [Notes - Groups HT23, Cayley tables](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/cayley-tables/)
- [Notes - Groups HT23, Homomorphisms](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/homomorphisms/)
- [Notes - Groups HT23, Subgroups](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/subgroups/)
- [Notes - Groups HT23, Permutations](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/permutations/)
- [Notes - Groups HT23, Cyclic groups](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/cyclic-groups/)
- [Notes - Groups HT23, Modular arithmetic](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/modular-arithmetic/)
- [Notes - Groups HT23, HCF and LCM](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/hcf-and-lcm/)
- [Notes - Groups HT23, Lagrange’s theorem](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/lagranges-theorem/)
- [Notes - Groups HT23, Equivalence relations](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/equivalence-relations/)
- [Notes - Groups HT23, Cosets](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/cosets/)
- [Notes - Groups HT23, Normal subgroups](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/normal-subgroups/)
- [Notes - Groups HT23, Special groups](https://ollybritton.com/notes/uni/prelims/ht23/groups/notes/special-groups/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/25608/mod_assign/introattachment/0/Sheet1-01.pdf?forcedownload=1)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/25609/mod_assign/introattachment/0/Sheet2-01.pdf?forcedownload=1)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/25610/mod_assign/introattachment/0/Sheet3-01.pdf?forcedownload=1)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/25611/mod_assign/introattachment/0/Sheet4-01.pdf?forcedownload=1)

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