We continue our discussion of groups and permutations, breaking down a permutation into disjoint cycles, finding a proper subgroup of even permutations in a group of order 2(2k + 1), and discussing properties of the orbits, stabilizers, fixes, etc…
In the previous entry More Introductory Group Theory, we introduced the definition of a group and also provided some lemmas to help us understand their basic structure a little better. It wasn’t as thorough as what you’d find in most Abstract Algebra books, though. But we did manage to introduce various morphisms, or maps between groups that preserve parts of their structure. Here we’ll continue with that theme…
We’ve already introduced some of the topics of Group Theory. In this entry we’ll talk about Lagrange’s Theorem, various morphisms, and try to tie it back to our ongoing discussion of permutations. We’ll also give some examples of groups…
