Exam Revision Flashcards
What are the subring criteria
Give the definition of an integral domain
Give the definition of a unit
Give the definition of irreducible
State Gauss’ Lemma
State Eisenstein’s Criterion
Give the definition of prime
How to prove a homomorphism is a injective
Give the criteria for ideals matching
Give the definition of prime and maximal ideals
What rings are PIDs
What is the CRT for rings
State Lagrange’s Theorem
State the normality criteria
Give the definition of conjugacy
Define the kernel of a homomorphism
A group of order p is isomorphic to
What do isomorphisms preserve
Give the criteria for subgroups to isomorphic to the parent group
State Cayley’s Theorem
State how orbits partition the set
State the orbit stabliser theorem
State the corollary of the OS theorem
State Cauchy’s Theorem
Groups of order 2p classification theorem
What the conjugacy classes in Sn
What are conjugacy classes in An
What is the relationship between normality and ccls
When is the centre non trivial
Give the p^2 classification theorem
State Sylow’s Theorem
State the fundamental theorem of finitely generated groups
Give the formula for number of cycles of shape [m1, m2, .., mr]
Give the formula for cycles of shape [m1,…,m1,m2..,m2…mr..mr]
