Everything about Hamiltonian Group totally explained
In
group theory, a
Dedekind group is a
group G such that every
subgroup of
G is
normal.All
abelian groups are Dedekind groups.
A non-abelian Dedekind group is called a
Hamiltonian group.
The most familiar (and smallest) example of a Hamiltonian group is the
quaternion group of order 8, denoted by
Q8.
It can be shown that every Hamiltonian group is a
direct product of the form
G =
Q8 ×
B ×
D, where
B is the direct sum of some number of copies of the
cyclic group C2, and
D is a
periodic abelian group with all elements of odd order.
Dedekind groups are named after
Richard Dedekind, who investigated them in a paper published in 1897, proving a form of the above structure theorem (for finite groups). He named the non-abelian ones after
William Rowan Hamilton, the discoverer of
quaternions.
Further Information
Get more info on 'Hamiltonian Group'.
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