### Meta

### Categories

- algebra (46)
- arithmetic (80)
- books (30)
- calculus (7)
- challenges (57)
- combinatorics (26)
- complex numbers (6)
- computation (80)
- convergence (9)
- counting (36)
- famous numbers (48)
- fibonacci (18)
- fractals (13)
- games (34)
- geometry (71)
- golden ratio (8)
- group theory (28)
- humor (7)
- induction (8)
- infinity (19)
- iteration (24)
- links (76)
- logic (9)
- meta (43)
- modular arithmetic (30)
- number theory (106)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (103)
- people (21)
- pictures (71)
- posts without words (34)
- primes (55)
- probability (9)
- programming (20)
- proof (87)
- puzzles (18)
- recursion (16)
- review (21)
- sequences (28)
- solutions (31)
- teaching (14)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- September 2019 (2)
- August 2019 (3)
- July 2019 (5)
- May 2019 (4)
- April 2019 (2)
- March 2019 (3)
- February 2019 (3)
- January 2019 (4)
- November 2018 (3)
- October 2018 (4)
- September 2018 (4)
- August 2018 (6)
- July 2018 (2)
- June 2018 (5)
- May 2018 (3)
- April 2018 (5)
- March 2018 (4)
- February 2018 (3)
- January 2018 (4)
- December 2017 (3)
- November 2017 (3)
- October 2017 (1)
- September 2017 (1)
- July 2017 (4)
- June 2017 (4)
- May 2017 (9)
- April 2017 (7)
- March 2017 (5)
- February 2017 (4)
- January 2017 (3)
- December 2016 (4)
- November 2016 (6)
- October 2016 (6)
- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

# Tag Archives: subgroups

## MaBloWriMo 30: Cyclic subgroups

Today, to wrap things up, we will use Lagrange’s Theorem to prove that if is an element of the group , the order of evenly divides the order of . So we have a group and an element . In … Continue reading

Posted in algebra, group theory, proof
Tagged cyclic, groups, Lagrange, MaBloWriMo, proof, subgroups
6 Comments

## MaBloWriMo 27: From subgroups to equivalence relations

Again, let be a group and a subgroup of . Then we can define a binary relation on elements of , called , as follows: if and only if there is some such that . That is, for any two … Continue reading

Posted in algebra, group theory, proof
Tagged equivalence, groups, Lagrange, MaBloWriMo, proof, relation, subgroups

## MaBloWriMo 26: Left cosets

Let be a group and a subgroup of . Then for each element we can define a left coset of by . That is, is the set we get by combining (on the left) with every element of . For … Continue reading

Posted in algebra, group theory, proof
Tagged cosets, groups, Lagrange, MaBloWriMo, proof, subgroups
1 Comment

## MaBloWriMo 25: Subgroups

So in the remainder of the month, we’ll prove that in any group , the order of each element must evenly divide the order (size) of the group. I said in an earlier post that this is called Lagrange’s Theorem; … Continue reading

Posted in algebra, group theory, proof
Tagged groups, Lagrange, MaBloWriMo, proof, subgroups
1 Comment