Literatur
For this terminology see for instance H. Zassenhaus, Lehrbuch der Gruppentheorie I, p. 104.
For the definition of this term see O. Ore, On the Foundation of Abstract Algebra I. Annals of Mathematics vol. 36 (1935) pp. 406–437.
An explicit example where the composition groups do not form a structure would be of some interest.
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Ore, O. A remark on groups which are the direct product of their sylow groups. Monatsh. f. Mathematik und Physik 48, 41–42 (1939). https://doi.org/10.1007/BF01696162
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DOI: https://doi.org/10.1007/BF01696162