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A non-abelian 2-group whose endomorphisms generate a ring, and other examples of E-groups

Published online by Cambridge University Press:  20 January 2009

J. J. Malone
J. J. Malone
Affiliation:
Worcester Polytechnic InstituteWorcester, Massachusetts 01609United States of America
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Groups for which the distributively generated near-ring generated by the endomorphisms is in fact a ring are known as E-groups and are discussed in (3). R. Faudree in (1) has given the only published examples of non-abelian E-groups by presenting defining relations for a family of p–groups. However, as shown in (3), Faudree's group does not have the desired property when p = 2.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 1 , February 1980 , pp. 57 - 59
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1) Faudree, R., Groups in which each element commutes with its endomorphic images, Proc. Amer. Math. Soc. 27 (1971), 236–240.Google Scholar
(2) Jonah, D. and Konvisser, M., Some non-abelian p-groups with abelian automorphism groups, Arch. Math. (Basel) 26 (1975), 131–133.Google Scholar
(3) Malone, J. J., More on groups in which each element commutes with its endomorphic images, Proc. Amer. Math. Soc. 65 (1977), 209–214.CrossRefGoogle Scholar
(4) Maxson, C. J., On groups and endomorphism rings, Math. Z. 122 (1971), 294–298.CrossRefGoogle Scholar
(5) McQuarrie, B. C. and Malone, J. J., Endomorphism rings of non-abelian groups, Bull. Austral. Math. Soc. 3 (1970), 349–352.Google Scholar
(6) Schenkman, E., Group Theory (D. Van Nostrand, 1965).Google Scholar