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On central endomorphisms of a group | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 4، شماره 3، آذر 2015، صفحه 1-5 اصل مقاله (178.09 K) | ||
| نوع مقاله: Ischia Group Theory 2014 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.9970 | ||
| نویسنده | ||
| Alessio Russo* | ||
| Seconda Universita di Napoli | ||
| چکیده | ||
| Let $\Gamma$ be a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$, and assume that $Inn(G)\leq \Gamma$. An endomorphism $\sigma$ of $G$ is said to be $\Gamma$-central if $\sigma$ induces the the identity on the factor group $G/C_G(\Gamma)$. Clearly, if $\Gamma=Inn(G)$, then a $\Gamma$-central endomorphism is a central endomorphism. In this article the conditions under which a $\Gamma$-central endomorphism of a group is an automorphism are investigated. | ||
| کلیدواژهها | ||
| central endomorphism؛ autocentral endomorphism؛ purely non-abelian group | ||
| مراجع | ||
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J. E. Adney and T. Yen (1965) Automorphisms of a p-group Il linois J. Math. 9, 137-143
H. Dietrich and P. Moravec (2011) On the autocomutator subgroup and absolute centre of a group J. Algebra 341, 150-157
G. Endimioni (2004) Hopficity and Co-hopficity in soluble groups Ukrainian Math. J. 56, 1594-1601
S. Franciosi, F. de Giovanni and M. L. Newell (1994) On central automorphisms of infinite groups Comm. Algebra 22, 2559-2578
F. de Giovanni, M. L. Newell and A. Russo (2014) A note on fixed p oints of automorphisms of infinite groups Int. J. Group Theory 3 (4), 57-61
P. Hall (1940) The classification of prime-p ower groups J. Reine Angew. Math. 182, 130-141
P. Hegarty (1994) The absolute centre of a group J. Algebra 169, 929-935
M. R. R. Moghaddam and H. Safa (2010) Some properties of autocentral automorphisms of a group Ric. Mat. 59, 257-264
D. J. S. Robinson (1996) A Course in the theory of groups Springer-Verlag, New York
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