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Remarks on the isomorphism problem in theories of construction of finite groups

Published online by Cambridge University Press:  24 October 2008

D. R. Taunt
D. R. Taunt
Affiliation:
Jesus CollegeCambridge
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Extract

In most theories for the construction of finite groups with given properties a major difficulty is the ‘isomorphism problem’, which consists of specifying how one representative of each class of isomorphic groups may be selected from the totality of groups constructed by the process laid down. To do this we need a practical criterion for the isomorphism of two constructed groups. The main object of the present paper is to establish such a criterion in a particular case, which in spite of its simplicity is important because it gives a method for the construction of A-groups (i.e. soluble groups whose Sylow subgroups are all Abelian). All soluble groups of cube-free order are included in this class of groups, and to exemplify the application of the criterion we summarize that part of our unpublished dissertation (7) which deals in detail with the groups of order 22.32.52.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 16 - 24
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Brahana, H. R.Finite metabelian groups and the lines of a projective four-space. Amer. J. Math. 73 (1951), 539–55.CrossRefGoogle Scholar
(2)Hall, P.A contribution to the theory of groups of prime-power order. Proc. Lond. math. Soc. (2), 36 (1933), 29–95.Google Scholar
(3)Hall, P.The construction of soluble groups. J. reine angew. Math. 182 (1940), 206–14.CrossRefGoogle Scholar
(4)Lunn, A. C. and Senior, J. K.Determination of the groups of orders 162–215, omitting order 192. Amer. J. Math. 57 (1935), 254–60.Google Scholar
(5)Speiser, A.Die Theorie der Gruppen von endlicher Ordnung, 3rd ed. (Berlin, 1937; New York, 1945).Google Scholar
(6)Taunt, D. R.On A-groups. Proc. Camb. phil. Soc. 45 (1949), 24–42.CrossRefGoogle Scholar
(7)Taunt, D. R. Ph.D. dissertation, University of Cambridge, 1949.Google Scholar
(8)Wielandt, H.Eine Kennzeichnung der direkten Produkte von p–Gruppen. Math. Z. 41 (1936), 281–2.CrossRefGoogle Scholar