There are many groups with these properties, as any locally finite group is amenable.

Wu also extended the classification of Suzuki et al. to locally finite groups.

Locally finite groups satisfy a weaker form of Sylow's theorems.

Every subgroup of a locally finite group is locally finite.

The class of locally finite groups is closed under subgroups, quotients, and extensions .

A locally finite group is a group for which every finitely generated subgroup is finite.

The class of locally finite groups behaves somewhat similarly to the class of finite groups.

Since all locally finite groups are periodic, this means that for linear groups and periodic groups the conditions are identical.

In this section G will denote a finite group, though some aspects generalize to locally finite groups and to profinite groups.

Sylow subgroups, Carter subgroups, and abelian subgroups of locally finite groups have been studied.

Since the cyclic subgroups of a locally finite group are finite, every element has finite order, and so the group is periodic.

While this need not be true in general, a result of Philip Hall and others is that every infinite locally finite group contains an infinite abelian group.

If a locally finite group has a finite p-subgroup contained in no other p-subgroups, then all maximal p-subgroups are finite and conjugate.

In mathematics, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous to a finite group.

His main interest was locally finite groups where he used his wide knowledge of finite groups to prove properties of infinite groups which shared some of the features of finite groups.

Much of the 1960s theory of formations and Fitting classes, as well as the older 19th century and 1930s theory of Sylow subgroups has an analogue in the theory of locally finite groups .

If there are finitely many conjugates, then the number of conjugates is congruent to 1 modulo p. In fact, if every countable subgroup of a locally finite group has only countably many maximal p-subgroups, then every maximal p-subgroup of the group is conjugate .