nLab elementary group

Idea

In the context of finite groups, an elementary group is one isomorphic, for some prime number $p$, to the direct product of

• a $p$-primary group

with

• a cyclic group whose order is relatively prime to $p$.

The concept of elementary subgroups, that is of subgroups that are elementary as groups, is used in some variants of the Brauer induction theorem.

Related entries

• Brauer induction theorem

• Artin induction theorem

References

See also:

• Wikipedia: Elementary group