nilpotent group

All nilpotent groups of class 3 or less are metabelian.

A nilpotent group is one that has a central series of finite length.

It is also true that finite nilpotent groups are supersolvable.

In a nilpotent group, every chief factor is centralized by every element.

The torsion elements in a nilpotent group form a normal subgroup.

In fact, a group has a central series if and only if it is a nilpotent group.

These can be particularly useful in the study of solvable groups and nilpotent groups.

Conversely, every finite nilpotent group is the direct product of p-groups.

Many properties of nilpotent groups are shared by hypercentral groups.

The rank problem is decidable for finitely generated nilpotent groups.

The direct product of two nilpotent groups is nilpotent.

Every nilpotent group, and more generally, every solvable group, is thin.

The Heisenberg group is an example of non-abelian, infinite nilpotent group.

Let G be a finitely generated torsionfree nilpotent group.

More generally, all nilpotent groups are solvable.

A nilpotent group G is a group with a lower central series terminating in the identity subgroup.

There are many unstable nilpotent groups.

A nilpotent group is one whose lower central series terminates in the trivial subgroup after finitely many steps.

Like solvable groups, nilpotent groups are too messy to classify except in a few small dimensions.

There are various connections between the lower central series and upper central series , particularly for nilpotent groups.

Every nilpotent group or Lie algebra is Engel.

Nilpotent groups and their generalizations, Trans.

It is a non-abelian nilpotent group.

In group theory, a nilpotent group is a group that is "almost abelian".

Every finitely generated nilpotent group is supersolvable.