Singapore Maths Tuition
For beginners in Group Theory, the basic method to prove that a subgroup is normal in a group is to show that “left coset = right coset”, i.e. 217 more words
1 month, 4 weeks ago
Think for yourself
in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.
798 more words
2 months, 3 weeks ago
in which we explore conjugacy classes in and , and prove that is simple.
518 more words
in which we explore groups of order 6 and make a start on quotients.
834 more words
3 months, 1 week ago
in which we apply group theory to prove Fermat-Euler, use Lagrange to help us find subgroups or determine what a small group must look like, and meet normal subgroups. 868 more words
Let be a subgroup of index 2.
Let and .
If , then , and , hence left coset equals to right coset.
If , then (set minus), and also , thus left coset also equals to right coset. 31 more words
6 months ago
in which we meet the quaternions and start exploring matrix groups.
621 more words
1 year, 2 months ago