Computation of isomorphism classes of -groups

Authors:
Rodney James and John Cannon

Journal:
Math. Comp. **23** (1969), 135-140

MSC:
Primary 20.40

MathSciNet review:
0238953

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Abstract: -groups may be classified by splitting the groups up into classes having the same commutator relations (isoclinism classes) and then determining the nonisomorphic groups in each class. This paper reduces the problem of determining the isomorphism classes to that of finding the equivalence classes of a set of matrices under some equivalence relation. A computer is used to find the equivalence classes for the first few values of , and these are then used as a guide for finding the solution for general .

**[1]**N. Blackburn,*On a special class of 𝑝-groups*, Acta Math.**100**(1958), 45–92. MR**0102558****[2]**T. Easterfield,*A Classification of Groups of Order*, Ph.D. Dissertation, Cambridge Univ., Cambridge, 1940.**[3]**Marshall Hall Jr. and James K. Senior,*The groups of order 2ⁿ(𝑛≤6)*, The Macmillan Co., New York; Collier-Macmillan, Ltd., London, 1964. MR**0168631****[4]**P. Hall,*The classification of prime-power groups*, J. Reine Angew. Math.**182**(1940), 130–141. MR**0003389****[5]**R. James,*The Groups of Order*, Ph.D. Thesis, Univ. of Sydney, 1968.**[6]**O. Schreier, ``Über die Erweiterung von Gruppen. II,''*Abh. Math. Sem. Univ. Hamburg*, v. 4, 1926, pp. 321-346.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1969-0238953-8

Article copyright:
© Copyright 1969
American Mathematical Society