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Section Results

This page contains theorems and propositions used throughout the course.

Subsection Results

Proposition 12 Basic Group Properties
Proposition 13 Socks-Shoes Principle
Theorem 17 Two-Step Subgroup Test
Theorem 18 One-Step Subgroup Test
Theorem 21 Center is a Subgroup
Proposition 26 \(K_4\) is the Smallest Non-Cyclic Group
Theorem 27 Equality of Powers of Group Elements
Theorem 28 Fundamental Theorem of Cyclic Groups
Theorem 31 Subgroups Generated by Powers of an Element
Theorem 38 Every Permutation is a Product of Disjoint Cycles
Theorem 39 Disjoint Cycles Commute
Theorem 40 Order of a Permutation
Theorem 41 Every Permutation is a Product of Transpositions
Proposition 42 Canonical Generators of \(S_n\)
Theorem 43 Always Even or Always Odd