#### Alladi Ramakrishnan Hall

#### Variations and Implications of a Theorem of Jordan

#### K N Raghavan

##### IMSc

*A theorem of Jordan dating from 1872, algorithmic aspects of which formed the subject of Arvind's lecture in FACETS last week, states that a group that acts transitively on a non-singleton finite set contains an element with no
fixed points.*

I this talk we will:

- prove the theorem and a quantified version of it
- apply these to group theory, topology, and number theory

With apology to experts, we will assume as little as possible so as to make the talk widely accessible, in particular to graduate students.