Semidirect products of $I$-$E$ groups
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- by Carter G. Lyons and Gary L. Peterson
- Proc. Amer. Math. Soc. 123 (1995), 2353-2356
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249885-8
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Abstract:
An I-E group is a group G in which the endomorphism near-ring generated by the inner automorphisms of G equals the endomorphism near-ring generated by the endomorphisms of G. In this paper we obtain a result characterizing when a semidirect product of I-E groups of relatively prime orders is an I-E group. We then use this result to show that a semidirect product of cyclic groups of relatively prime orders is an I-E group.References
- A. Fröhlich, The near-ring generated by the inner automorphisms of a finite simple group, J. London Math. Soc. 33 (1958), 95–107. MR 93543, DOI 10.1112/jlms/s1-33.1.95
- J. J. Malone and C. G. Lyons, Finite dihedral groups and d.g. near rings. I, Compositio Math. 24 (1972), 305–312. MR 308206
- J. J. Malone and C. G. Lyons, Finite dihedral groups and d.g. near rings. II, Compositio Math. 26 (1973), 249–259. MR 330236
- J. J. Malone and Gordon Mason, $\textrm {ZS}$-metacylic groups and their endomorphism near-rings, Monatsh. Math. 118 (1994), no. 3-4, 249–265. MR 1309651, DOI 10.1007/BF01301692
- J. D. P. Meldrum, On the structure of morphism near-rings, Proc. Roy. Soc. Edinburgh Sect. A 81 (1978), no. 3-4, 287–298. MR 516420, DOI 10.1017/S0308210500010623
- Derek John Scott Robinson, A course in the theory of groups, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR 648604, DOI 10.1007/978-1-4684-0128-8
- W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2353-2356
- MSC: Primary 16Y30; Secondary 20E36
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249885-8
- MathSciNet review: 1249885