Tags » Normal Subgroup

Advanced Method for Proving Normal Subgroup

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

Group Theory

Groups Lecture 18

in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.
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Groups

Groups Lecture 17

in which we explore conjugacy classes in and , and prove that is simple.
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Groups

Groups Lecture 11

in which we explore groups of order 6 and make a start on quotients.
834 more words

Groups

Groups Lecture 10

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

Groups

Proof that any subgroup of index 2 is normal

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

Group Theory

Groups Lecture 18

in which we meet the quaternions and start exploring matrix groups.
621 more words

Groups