mathematics, specifically group theory, a subgroup series of a group G {\displaystyle G} is a chain of subgroups: 1 = A 0 ≤ A 1 ≤ ⋯ ≤ A n = G {\displaystyle...

a composition series is a maximal subnormal series, while a chief series is a maximal normal series. If a group G has a normal subgroup N, then the factor...

the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator...

commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory...

normal subgroup of G/Ni. Equivalently, there does not exist any subgroup A normal in G such that Ni < A < Ni+1 for any i. In other words, a chief series may...

for any pair g, h ∈ G. ascendant subgroup A subgroup H of a group G is ascendant if there is an ascending subgroup series starting from H and ending at G...

is any of certain special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p-core of a group. For a group...

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...