View source for MA 453 Spring 2009 Walther Definitions - Rhea

[[Category:MA453Spring2009Walther]]

Euclid
a = qb + r with 0 <= r < b
where a,b,q,r are integers

--ERaymond 12:26  29 January 2009 (UTC)

<p><b>GCD:</b>
The greatest common divisor of two nonzero integers a and b is the largest of all common divisors of a and b.
</p>

'''LCM:''' The least common multiple of two nonzero integers a and b is the smallest positive integer that is a multiple of both a and b. 

--[[User:Jmcdorma|Jmcdorma]] 12:16, 5 February 2009 (UTC)

Monomorphism: morphism for which phi(g) = phi(g') happens only if g = g'. (injective)

Epimorphism: morphism for which every element in target group H is hit. (surjective)

Isomorphism: morphism that is both injective and surjective.

The kernel of a morphism is the collection of elements in G that satisfy phi(g) = 1_H

An inner automorphism, Inn(G), is always attached to some group element written ϕ_{a} for the following morphism from G to itself: ϕ_{a}(g)=aga⁻¹


If m and n are coprime, then Z_mn is isomorphic to Z_m x Z_n

The stabilizer of a point P is the set of elements in a group G of permutations that keep P in the same place; it is a subgroup of G.

The orbit of a point P is the set of all points to which P can be moved using an element of a group G of permutations.