## 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 |
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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 |