Automorphism groups emitting local endomorphism near-rings

Peterson, Gary L.

doi:10.1090/S0002-9939-1989-0952320-5

Automorphism groups emitting local endomorphism near-rings
HTML articles powered by AMS MathViewer

by Gary L. Peterson PDF

Proc. Amer. Math. Soc. 105 (1989), 840-843 Request permission

Abstract:

The question of whether a group of automorphisms $A$ containing the inner automorphisms of a nonabelian $p$-group $G$ can generate a local endomorphism near-ring when $A$ is not a $p$-group is considered. Conditions on $A$ are obtained which give us that the endomorphism near-ring generated by $A$ is not local. An example is given showing that the endomorphism near-ring generated by $A$ can be local when these conditions are not met.

References

Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
Graham Higman, Suzuki $2$-groups, Illinois J. Math. 7 (1963), 79–96. MR 143815
Bertram Huppert and Norman Blackburn, Finite groups. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 242, Springer-Verlag, Berlin-New York, 1982. AMD, 44. MR 650245
J. D. P. Meldrum and C. Lyons, Characterizing series for faithful d.g. near-rings, Proc. Amer. Math. Soc. 72 (1978), no. 2, 221–227. MR 507312, DOI 10.1090/S0002-9939-1978-0507312-X
Carter G. Lyons and Gary L. Peterson, Local endomorphism near-rings, Proc. Edinburgh Math. Soc. (2) 31 (1988), no. 3, 409–414. MR 969070, DOI 10.1017/S0013091500006805
J. D. P. Meldrum, Near-rings and their links with groups, Research Notes in Mathematics, vol. 134, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 854275
Gary L. Peterson, On the structure of an endomorphism near-ring, Proc. Edinburgh Math. Soc. (2) 32 (1989), no. 2, 223–229. MR 1001120, DOI 10.1017/S0013091500028625