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Some special classes of n-Aabelian groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 1، شماره 2، شهریور 2012، صفحه 19-24 اصل مقاله (278.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.474 | ||
| نویسندگان | ||
| Costantino Delizia1؛ Antonio Tortora* 2 | ||
| 1Dipartimento di Matematica Università di Salerno - Italy | ||
| 2Dipartimento di Matematica, Università di Salerno - Italy | ||
| چکیده | ||
| Given an integer $n$, we denote by $\mathfrak B_n$ and $\mathfrak C_n$ the classes of all groups $G$ for which the map $\phi_{n}:g\mapsto g^n$ is a monomorphism and an epimorphism of $G$, respectively. In this paper we give a characterization for groups in $\mathfrak B_n$ and for groups in $\mathfrak C_n$. We also obtain an arithmetic description of the set of all integers $n$ such that a group $G$ is in $\mathfrak B_n\cap\mathfrak C_n$. | ||
| کلیدواژهها | ||
| n-abelian group؛ abelian group؛ finite exponent | ||
| مراجع | ||
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J. L. Alperin (1969) A classification of n-abelian groups Canad. J. Math. 21, 1238-1244
R. Baer (1953) Factorization of n-soluble and n-nilpotent groups Proc. Amer. Math. Soc. 4, 15-26
L.-C. Kappe (1986) On n-Levi groups Arch. Math. 47, 198-210
F. W. Levi (1945) Notes on group theory VII J. Indian Math. Soc. 9, 37-42
D. MacHale (1974) Power mappings and group morphisms Proc. Roy. Irish. Acad. Sect. A 74, 91-93
E. Schenkman and L. I. Wade (1958) The mapping which takes each element of a group onto its nth power Amer. Math. Monthly 65, 33-34
H. F. Trotter (1965) Groups in which raising to a power is an automorphism Canad. Math. Bull. 8, 825-827
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