Visual Algebra, Lecture 3.6: Conjugate subgroups скачать в хорошем качестве

Visual Algebra, Lecture 3.6: Conjugate subgroups

We will continue to study conjugacy classes of subgroups. We’ll start by learning about “unicorn subgroups”, a definition new to this video series and my book. This will help us identify normal subgroups by inspection, just from the subgroup lattice. We will prove some basic algebraic results about conjugate subgroups, and then explore how to find them and what they look like in a Cayley graph. Along the way, we'll see two non isomorphic groups of the same order than have the same subgroup lattice. Course & book webpage (with complete lecture note slides, HW, exams, etc.): https://www.math.clemson.edu/~macaule... ------------------------------------------------------------------------------------------------------------------------------------------------------ CHAPTERS 0:00 Introduction 0:33 Normal subgroups of order 2 4:15 Unicorn subgroups 7:59 Conjugating normal subgroups 9:58 Finding conjugacy classes by inspection 11:40 Unicorns in the diquaternion group 16:55 A mysterious group of order 16 20:31 The abelian group C₈× C₂ 21:51 The semiabelian group SA₈ 24:06 Left cosets vs. right cosets 29:01 Cosets and conjugate subgroups 33:17 Conjugating a normal subgroup of C₄⋊ C₄ 36:32 Conjugating a non-normal subgroup of C₄⋊ C₄ 41:30 The subgroup lattice of C₄⋊ C₄