The subgroup method is an algorithm used in the
mathematical field of
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
. It is used to find the
word
A word is a basic element of language that carries an semantics, objective or pragmatics, practical semantics, meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of w ...
of an element. It doesn't always return the minimal word, but it can return optimal words based on the
series of subgroups that is used. The code looks like this:
function operate(element, generator)
function subgroup(g)
sequence := (set of subgroups that will be used, depending on the method.)
word := []
for subgroup in sequence
coset_representatives := []
for operation in coset_representatives
if operate(g, operation) is in the next subgroup then
append operation onto word
g = operate(g, operation)
break
return word
Group theory
{{Abstract-algebra-stub