Abstract
Example 2.3.(Group commutators) Let G be a group, and let AG be the underlying set of G
with operation [x, y]:= xyx− 1y− 1. For brevity, let us call prime elements of the algebra AG
prime elements of G. These are elements of G not representable as a single commutator.
Denote by [G, G] the subgroup of G generated by all commutators [x, y], x, y∈ G, and recall
that G is said to be perfect if [G, G]= G.
with operation [x, y]:= xyx− 1y− 1. For brevity, let us call prime elements of the algebra AG
prime elements of G. These are elements of G not representable as a single commutator.
Denote by [G, G] the subgroup of G generated by all commutators [x, y], x, y∈ G, and recall
that G is said to be perfect if [G, G]= G.
| Original language | American English |
|---|---|
| Pages (from-to) | 5-13 |
| Number of pages | 9 |
| Journal | European Mathematical Society Magazine |
| Volume | 2020-12 |
| Issue number | 118 |
| DOIs | |
| State | Published - 1 Dec 2020 |