Endomorphism rings of non-abelian groups

Autor:	J. J. Malone, B. C. McQuarrie
Rok vydání:	1970
Předmět:	Pure mathematics Torsion subgroup Solvable group Group (mathematics) General Mathematics Cyclic group Elementary abelian group Abelian group Divisible group Non-abelian group Mathematics
Zdroj:	Bulletin of the Australian Mathematical Society. 3:349-352
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972700046049
Popis:	In 1942 F.W. Levi described those groups in which any two inner automorphic images of an arbitrary element commute. Until recently it was not known whether there existed non-abelian groups with the property that any two endomorphic images of an arbitrary element commute. Now, R. Faudree has given examples of finite p–groups having this property. In this paper we give a necessary and sufficient condition that a torsion group which contains no elements of order 2 has this property. The technique of proof involves looking at certain near rings of functions on the group. The inspiration for the theorem comes from the “halving” technique used by B.H. Neumann in 1940.
Databáze:	OpenAIRE
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