Tags » Group Theory

Van Kampen diagrams: an application to tiling problems

In this note, we are interested in the following problem: given a chessboard and a set of dominoes, is it possible to tile our chessboard using the dominoes we have? 825 more words

Group Theory

A Generalization of Wilson's Theorem (due to Gauss)

John Wilson (1741-1793) was a well-known English mathematician in his time, whose legacy lives on in his eponymous result, Wilson’s Theorem. To recall, this is the statement that an integer is prime if and only if… 1,015 more words

Number Theory

Relations & Their Relatives : 11

Re: Peirce List DiscussionJeffrey Brian Downard

In discussing the “combinatorial explosion” of dyadic relations that takes off in passing from a universe of two elements to a universe of three elements, I made the following observation: 200 more words



June 26 – 177

In finite geometry, a Fano plane is a finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point. 35 more words

One Image A Day - 364 Days

Universal acylindrical actions

I’m at a fantastic summer graduate school at MSRI (the Mathematical Sciences Research Institute, a.k.a. “math heaven”) right now and re-met a friend I’d seen at a few earlier conferences.   905 more words


Observations about the symmetric groups

Recall that the nth symmetric group consists of all permutations of the set {1,…,n}.

An easier way to multiply elements. Let’s use (1 2)(2 3) again and see, working left to right, where each number is sent.  1,334 more words

Group Theory

Scientific American article about finite simple groups

For those of you who are a bit rusty: a finite group is a group that has a finite number of elements. A simple group is one that has no proper non-trivial normal subgroups (that is, only the identity and the whole group are normal subgroups). 140 more words

Advanced Mathematics