deepdream of
          a sidewalk
Show Answer
Math and science::Algebra::Aluffi

Groups. Some properties of order.

Property 1

Suppose that g2=e for all elements g in group G. Then we can say that G is [what?].

Property 2

Suppose g is an element with odd order. Then [what can be said about |g2|]?

Property 3

The order of [m]n in Z/nZ is 1 if n|m, and more generally:

|[m]n|=ngcd(m,n)

Property 4

Following from property 3:

  • The class [m]n generates Z/nZ iff gcd(m,n)=1.
  • the order of every element of Z/nZ divides n, which is the order, |Z/nZ|.