On an isomorphism problem for endomorphism near-rings

Peterson, Gary

doi:10.1090/S0002-9939-98-04302-0

On an isomorphism problem for endomorphism near-rings
HTML articles powered by AMS MathViewer

by Gary L. Peterson PDF

Proc. Amer. Math. Soc. 126 (1998), 1897-1900 Request permission

Abstract:

Suppose $R$ and $S$ are endomorphism near-rings generated by groups of automorphisms containing the inner automorphisms of two respective finite perfect groups $G$ and $H$. In this note we show that if $R$ and $S$ are isomorphic, then $G/Z(G)$ and $H/Z(H)$ are isomorphic.

References

C. G. Lyons and Gordon Mason, Endomorphism near-rings of dicyclic and generalised dihedral groups, Proc. Roy. Irish Acad. Sect. A 91 (1991), no. 1, 99–111. MR 1173163
C. G. Lyons and J. D. P. Meldrum, $N$-series and tame near-rings, Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), no. 1-2, 153–163. MR 580254, DOI 10.1017/S0308210500012087
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
S. A. Syskin, On a problem of C. Lyons and G. Mason, to appear
S. D. Scott, Tame near-rings and $N$-groups, Proc. Edinburgh Math. Soc. (2) 23 (1980), no. 3, 275–296. MR 620925, DOI 10.1017/S0013091500003837
S. D. Scott, On the finiteness and uniqueness of certain $2$-tame $N$-groups, Proc. Edinburgh Math. Soc. (2) 38 (1995), no. 2, 193–205. MR 1335870, DOI 10.1017/S0013091500019040