Groups Week 2 22/23

Welcome to our activities for Week 2 (the week of September 12).
In terms of building knowledge of Group Theory, there are three goals this week.
  • To expand our collection of examples from Week 1, especially with groups of symmetries and groups of permutations.
  • To study the axiomatic definition of a group, and to relate each of the examples that we have encountered so far to that. A good exercise for getting a sense of what this definition is for, is to use it to decide whether a given algebraic structure is a group or not. There will be some tasks like this on the first homework sheet, which will appear next week.
  • To look at some further concepts from group theory, including that of a generating set.

Activity for Week 2 consists of the following steps.
  1. Have a look back at the examples from last week’s lectures, and at Section 1.1 of the lecture notes.
  2. Come to the lectures on Thursday and Friday, September 18 and 19.
    Slides for Thursday’s lecture: Lecture 3
    Slides for Friday’s lecture: Lecture 4
    Relevant sections of the lecture notes: Section 1.1, Section 1.2 If you cannot make it to the lectures, have a look at these videos from 2020/21 (as usual, please ignore any details that are particular to that year).

  3. By the end of this week, our position in the lecture notes will be somewhere in Section 1.3. There are some examples in the notes that are not discussed in the lectures, so have a look at them even if you have your own notes from the lectures.