关于K(n, 4)的自同态单群

Ars Comb. Pub Date : 2012-07-05 DOI:10.1142/S1005386712000302

Hailong Hou, Rui Gu

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引用次数: 4

摘要

本文明确地研究了循环完全图K(n,3)的自同态单阵。证明了阶数为n的二面体群AutK(n,3) =Dn，并证明了当3不除n时，K(n,3)是不可伸缩的，End(K(3m,3)) =qEnd(K(3m,3))， sEnd(K(3m,3)) =Aut(K(3m,3))， K(3m,3)是自同态正则的。刻画了End(K(3m,3))的结构，解决了End(K(n,3))的一些列举问题。

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On the endomorphism monoid of K(n, 4)

In this paper, the endomorphism monoid of circulant complete graph K(n,3) is explored explicitly. It is shown that AutK(n,3)) =Dn, the dihedral group of degree n. It is also shown that K(n,3) is unretractive when 3 does not divide n, End(K(3m,3)) =qEnd(K(3m,3)), sEnd(K(3m,3)) =Aut(K(3m,3)) and K(3m,3) is endomorphism-regular. The structure of End(K(3m,3)) is characterized and some enumerative problems concerning End(K(n,3)) are solved.

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Ars Comb.

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