An Algorithm for Constructing Finite Solvable Groups

Amiri Mehr, Sajad and Abdolzadeh, Hossein and Bahmanpour, Kamal (2018) An Algorithm for Constructing Finite Solvable Groups. Masters thesis, University of Mohaghegh Ardabili.

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Abstract

The construction of all groups of a given order is an old and fundamental topic in finite group theory. Given an ordrr n, the aim is to determine a list of groups of order n. So that every groupof order n is isomorphic to exactly on group in the list. In more recent years algorithms have beendeveloped for this purpose. Modern group construction algorithms distinguish non-solvable groups. Nilpotent groups are determined as direct products of p-groups and p-groups can be constructed usingthe p-group generation algorithm. Sovable groups can be determined by the Frattini extension method. Non-Solvable groups can be obtained via cyclic extansion of Perfect groups.

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