Abstract
AnI-E group is a group in which the endomorphism near-ring generated by the group's inner automorphisms equals the endomorphism near-ring generated by its endomorphisms. In this paper we shall completely determine the finite groups that are semidirect products of cyclic groups and areI-E groups.
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References
Huppert, B.: Endliche Gruppen I. Berlin: Springer. 1967.
Lyons, C. G., Malone, J. J.: Finite dihedral groups and d. g. near-rings. I. Compositio Math.24, 305–312 (1972).
Lyons, C. G., Malone, J. J.: Finite dihedral groups and d. g. near-rings. II. Compositio Math.26, 249–259 (1973).
Lyons, C. G., Peterson, G. L.: Local endomorphism near-rings. Proc. Edinb. Math. Soc.31, 409–414 (1988).
Lyons, C. G., Peterson. G. L.: Semidirect products ofI-E groups. Proc. Amer. Math. Soc., to appear.
Malone, J. J., Mason, G.: ZS-metacyclic groups and their endomorphism near-rings. Mh. Math.118, 249–265 (1994).
Maxson, C. J.: On local near-rings. Math. Z.106, 197–205 (1968).
Syskin, S. A., Thomsen, M. J.: The holomorph of a cyclicp-group and related nearrings. to appear.
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Peterson, G.L. The semidirect products of finite cyclic groups that areI-E groups. Monatshefte für Mathematik 121, 275–290 (1996). https://doi.org/10.1007/BF01298955
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DOI: https://doi.org/10.1007/BF01298955