The group of automorphisms of a distributively generated near ring

Author:
J. J. Malone

Journal:
Proc. Amer. Math. Soc. **88** (1983), 11-15

MSC:
Primary 16A76; Secondary 20F28

MathSciNet review:
691269

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: S. D. Scott has shown that the group of automorphisms of the near ring generated by the automorphisms of a given group is isomorphic to the automorphism group of the given group if that group's automorphism is complete. Here that theorem is generalized by showing that the group of automorphisms of a near ring distributively generated by its units is a subgroup of the group of automorphisms of the group of units. The results obtained are used to find the automorphism groups of certain near rings.

**[1]**Gerald Berman and Robert J. Silverman,*Near-rings*, Amer. Math. Monthly**66**(1959), 23–34. MR**0100002****[2]**R. Faudree,*Groups in which each element commutes with its endomorphic images*, Proc. Amer. Math. Soc.**27**(1971), 236–240. MR**0269737**, 10.1090/S0002-9939-1971-0269737-3**[3]**J. J. Malone,*Generalised quaternion groups and distributively generated near-rings*, Proc. Edinburgh Math. Soc. (2)**18**(1972/73), 235–238. MR**0316512****[4]**J. J. Malone,*A nonabelian 2-group whose endomorphisms generate a ring, and other examples of 𝐸-groups*, Proc. Edinburgh Math. Soc. (2)**23**(1980), no. 1, 57–59. MR**582023**, 10.1017/S0013091500003606**[5]**J. J. Malone and C. G. Lyons,*Endomorphism near-rings*, Proc. Edinburgh Math. Soc. (2)**17**(1970), 71–78. MR**0269703****[6]**Carlton J. Maxson,*On groups and endomorphism rings*, Math. Z.**122**(1971), no. 4, 294–298. MR**0396654****[7]**G. A. Miller, H. F. Blichfeldt and L. E. Dickson,*Theory and applications of finite groups*, Wiley, New York, 1916.**[8]**Günter Pilz,*Near-rings*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications; North-Holland Mathematics Studies, No. 23. MR**0469981****[9]**Eugene Schenkman,*Group theory*, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR**0197537****[10]**S. D. Scott,*The automorphism group of a near-ring*, Proc. Amer. Math. Soc.**80**(1980), no. 4, 560–562. MR**587927**, 10.1090/S0002-9939-1980-0587927-2**[11]**A. D. Thomas and G. V. Wood,*Group tables*, Shiva, Orpington, Kent, 1980.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A76,
20F28

Retrieve articles in all journals with MSC: 16A76, 20F28

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1983-0691269-7

Article copyright:
© Copyright 1983
American Mathematical Society