Suppose that are two subgroups of some ambient group , with the index of in being finite. Then is the union of left cosets of , thus for some set of cardinality . 1,036 more words

## Tags » Math.GR

#### The standard branch of the matrix logarithm

Because of Euler’s identity , the complex exponential is not injective: for any complex and integer . As such, the complex logarithm is not well-defined as a single-valued function from to . 1,105 more words

#### Additive limits

In graph theory, the recently developed theory of *graph limits* has proven to be a useful tool for analysing large dense graphs, being a convenient reformulation of the… 4,616 more words

#### A trivial generalisation of Cayley's theorem

One of the first basic theorems in group theory is Cayley’s theorem, which links abstract finite groups with concrete finite groups (otherwise known as… 870 more words

#### Hilbert's fifth problem and approximate groups

Due to some requests, I’m uploading to my blog the slides for my recent talk in Segovia (for the birthday conference of Michael Cowling) on “ 47 more words

#### Qualitative probability theory, types, and the group chunk and group configuration theorems

The classical foundations of probability theory (discussed for instance in this previous blog post) is founded on the notion of a probability space – a space (the… 7,853 more words

#### Expansion in finite simple groups of Lie type

Emmanuel Breuillard, Ben Green, Bob Guralnick, and I have just uploaded to the arXiv our joint paper “Expansion in finite simple groups of Lie type… 950 more words