Each other vs. one another

Hello everybody - and thank you so much for your invitation to this site, Torsten!
My question regards two similar phrases: “each other” and “one another”. My grammar book says they’re identical and are used to talk about two people. On the other hand I heard a respectable professor say that “each other” is used while talking about 2 people, and ‘one another’ is for larger groups. So, which explanation is right?


Each other and one another are often used interchangeably, with little difference in meaning. However, while each other can be used to emphasise the individuality of the relationship between one person or thing and another, one another can be used to focus on people and things as groups.