caa a22 4500 386386048 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198911 xx s 000 0 eng 10.1017/S0305004100068158 doi S0305004100068158 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100068158 Curtis R. T. School of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT Natural constructions of the Mathieu groups [Elektronische Daten] [R. T. Curtis] In the second half of the last century the French mathematician Emil Mathieu discovered two quintuply transitive permutation groups, now labelled M12 and M24, acting on twelve and twenty-four letters respectively. With the classification of finite simple groups complete we now know that any other quintuply transitive permutation group, on any number of letters, must contain the corresponding alternating group. Indeed, the only quadruply transitive groups, other than the alternating and symmetric groups, are the point stabilizers in M12 and M24, which are denoted by M11 and M23 respectively. To put it another way, the study of multiply (≥ 4-fold) transitive groups now means the study of the symmetric groups and the Mathieu groups. Apart from their beauty and interest in their own right the Mathieu groups are involved in many of the other sporadic simple groups: see ([2], p. 238). Thus a detailed understanding of the other exceptional groups necessitates an intimate knowledge of M12 and M24. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 423-429 0305-0041 106:3<423 1989 106 PSP https://doi.org/10.1017/S0305004100068158 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100068158 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Curtis R. T. School of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 423-429 0305-0041 106:3<423 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge