History of mathematics and history of mathematics education generate insights for didactical reflection (Artigue, 1991; Chorlay & De Hosson, 2016; Chorlay et al., 2022). This paper aims to present elements of history of mathematics education that will contribute to a PhD dissertation (A. Rolland) on the links between mathematical knowledge acquired in tertiary education and its use by secondary school teachers (a topic known as “Klein's second discontinuity”). The specific topic chosen is that of knowledge about group theory, and the aim of the PhD is to produce a capstone course, that is a programme for pre-service teachers training backed up by general methodological and theoretical reflections on Klein's second discontinuity. One of the challenges is to understand (and to help prospective teachers understand) the future role of abstract theories whose link with the content to be taught is not transparent. Rather than seeking to determine a priori (through mathematical and/or didactic reflection) what this role is in the case of groups, we are seeking, through a historical study of one of the main French competitive examinations for teacher recruitment (agrégation) from 1950 to 1990, to identify the expectations and motivations of the institution recruiting teachers with regard to future teachers. The choice of study period allows us to investigate variations in these expectations, showing that they may have been significant even before and after the New Maths period (Gispert, 2023).