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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 commutative.

Property 2

Suppose g is an element with odd order. Then |g2|=|g|?

Property 3

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

[|[m]n|=?? ]

Property 4

Following from property 3:

  • The class [m]n generates Z/nZ iff [what?].
  • the order of every element of Z/nZ [what can be said here?].