Power-commutator presentation
From Groupprops
Definition
A power-commutator presentation of a group for a prime number is a presentation with generating set for a totally ordered indexing set and relations of the form:
- power relations: is written as a product of powers of , with the s in increasing order as we go from left to right in the product. The exponent on for is denoted .
- commutator relations: The commutator is written as a product of powers of , with the s in increasing order as we go from left to right in the product. The exponent of for is denoted .
For a group of prime power order , a power-commutator presentation is termed consistent if it uses exactly generators.