Words for maximal Subgroups of <i>Fi</i><sub>24</sub>'

Abstract

Group Theory is the mathematical application of symmetry to an object to obtain knowledge of its physical properties. The symmetry of a molecule provides us with the various information, such as - orbitals energy levels, orbitals symmetries, type of transitions than can occur between energy levels, even bond order, all that without rigorous calculations. The fact that so many important physical aspects can be derived from symmetry is a very profound statement and this is what makes group theory so powerful. In group theory, a finite group is a mathematical group with a finite number of elements. A group is a set of elements together with an operation which associates, to each ordered pair of elements, an element of the set. In the case of a finite group, the set is finite. The Fischer groups Fi(22), Fi(23) and Fi(24)' are introduced by Bernd Fischer and there are 25 maximal subgroups of Fi(24)'. It is an open problem to find the generators of maximal subgroups of Fi(24)'. In this paper we provide the generators of 10 maximal subgroups of Fi(24)'.