
Recent Posts
Archives
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: free groups
Free Groups and Tiling
Introduction Consider the following simple problem. Prove that the shape on the left cannot be completely tiled by 20 polygons of the types shown on the right. The solution is rather simple: colour the shape in the following manner. This … Continue reading
Posted in Uncategorized
Tagged combinatorics, free groups, group theory, groups, polyominoes, tiling, words
Leave a comment
Intermediate Group Theory (6)
In this post, we’ll only focus on additive abelian groups. By additive, we mean the underlying group operation is denoted by +. The identity and inverse of x are denoted by 0 and –x respectively. Similarly, 2x+3y refers to x+x+y+y+y. Etc … Continue reading
Posted in Notes
Tagged abelian groups, advanced, direct products, direct sums, free groups, generated groups, universal properties
Leave a comment
Intermediate Group Theory (5)
Free Groups To motivate the concept of free groups, let’s consider some typical group G and elements a, b of G. Recall that , the subgroup generated by {a, b}, is defined to be the intersection of all subgroups of G containing a and b. Immediately, we see … Continue reading
Posted in Notes
Tagged advanced, free groups, generated groups, group theory, universal property
Leave a comment