The group of automorphisms of a distributively generated near ring
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- by J. J. Malone PDF
- Proc. Amer. Math. Soc. 88 (1983), 11-15 Request permission
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.References
- Gerald Berman and Robert J. Silverman, Near-rings, Amer. Math. Monthly 66 (1959), 23–34. MR 100002, DOI 10.2307/2309918
- R. Faudree, Groups in which each element commutes with its endomorphic images, Proc. Amer. Math. Soc. 27 (1971), 236–240. MR 269737, DOI 10.1090/S0002-9939-1971-0269737-3
- J. J. Malone, Generalised quaternion groups and distributively generated near-rings, Proc. Edinburgh Math. Soc. (2) 18 (1972/73), 235–238. MR 316512, DOI 10.1017/S0013091500009974
- 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, DOI 10.1017/S0013091500003606
- J. J. Malone and C. G. Lyons, Endomorphism near-rings, Proc. Edinburgh Math. Soc. (2) 17 (1970), 71–78. MR 269703, DOI 10.1017/S0013091500009214
- Carlton J. Maxson, On groups and endomorphism rings, Math. Z. 122 (1971), no. 4, 294–298. MR 396654, DOI 10.1007/BF01110163 G. A. Miller, H. F. Blichfeldt and L. E. Dickson, Theory and applications of finite groups, Wiley, New York, 1916.
- Günter Pilz, Near-rings, North-Holland Mathematics Studies, No. 23, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications. MR 0469981
- Eugene Schenkman, Group theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR 0197537
- S. D. Scott, The automorphism group of a near-ring, Proc. Amer. Math. Soc. 80 (1980), no. 4, 560–562. MR 587927, DOI 10.1090/S0002-9939-1980-0587927-2 A. D. Thomas and G. V. Wood, Group tables, Shiva, Orpington, Kent, 1980.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 11-15
- MSC: Primary 16A76; Secondary 20F28
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691269-7
- MathSciNet review: 691269