Question:Let G be a finite group, and suppose that H is normal subgroup
of G.
Show...
Question
Let G be a finite group, and suppose that H is normal subgroup
of G.
Show...
Let G be a finite group, and suppose that H is normal subgroup
of G.
Show that, for every g ∈ G, the order of gH in G/H must divide
the order of g in G.
What is the order of the coset [4]_{42} +
〈[6]_{42}〉 in Z_{42}/〈[6]_{42}〉?
Find an example to show that the order of gH in G/H does not
always determine the order of g in G. That is, find an example of a
group G, and a normal subgroup H is normal subgroup of G, and
elements g_{1},g_{2} ∈ G, such that g_{1}H
= g_{2}H but g_{1} and g_{2} do not have
the same order in G. Prove that your example has all of the
required properties.