Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T09:16:16.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite groups having unique proper characteristic subgroups. I

Published online by Cambridge University Press:  24 October 2008

D. R. Taunt
D. R. Taunt
Affiliation:
Jesus CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

It is well known that a characteristically-simple finite group, that is, a group having no characteristic subgroup other than itself and the identity subgroup, must be either simple or the direct product of a number of isomorphic simple groups. It was suggested to the author by Prof. Hall that finite groups possessing exactly one proper characteristic subgroup would repay attention. We shall call a finite group having a unique proper characteristic subgroup a ‘UCS group’. In the present paper we first give some results on direct products of isomorphic UCS groups, and then we consider in more detail one of the types of UCS groups which can exist, that consisting of groups whose orders are divisible by exactly two distinct primes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 25 - 36
Copyright
Copyright © Cambridge Philosophical Society 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hall, P.The construction of soluble groups. J. reine angew. Math. 182 (1940), 206–14.Google Scholar
(2)Taunt, D. R.On A-groups. Proc. Camb. phil. Soc. 45 (1949), 24–42.CrossRefGoogle Scholar
(3)Taunt, D. R.Remarks on the isomorphism problem in theories of construction of finite groups. Proc. Camb. phil. Soc. 51 (1955), 16–24.Google Scholar
(4)van der Waerden, B. L.Moderne Algebra, II, 2nd ed. (Berlin, 1940).CrossRefGoogle Scholar
(5)Weyl, H.The classical groups, 2nd ed. (Princeton, 1946).Google Scholar