Subgroup method
Encyclopedia
The subgroup method is an algorithm used in the mathematical field of group theory
. It is used to find the word 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
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
. It is used to find the word 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