The cycle index of the automorphism group of Zn | Zendy

Vladimir Božović | Zendy; Zana Kovijanic-Vukicevic | Zendy

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The cycle index of the automorphism group of Zn

Author(s) -

Vladimir Božović,

Zana Kovijanic-Vukicevic

Publication year - 2017

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1715099b

Subject(s) - modulo , mathematics , group (periodic table) , permutation group , combinatorics , automorphism , outer automorphism group , action (physics) , automorphism group , index (typography) , symmetric group , class (philosophy) , set (abstract data type) , discrete mathematics , group action , permutation (music) , computer science , physics , artificial intelligence , quantum mechanics , world wide web , acoustics , programming language

We consider the group action of the automorphism group Un = Aut(Zn) on the set Zn, that is the set of residue classes modulo n. Clearly, this group action provides a representation of Un as a permutation group acting on n points. One problem to be solved regarding this group action is to find its cycle index. Once it is found, there appears a vast class of related enumerative and computational problems with interesting applications. We provide the cycle index of specified group action in two ways. One of them is more abstract and hence compact, while another one is basically a procedure of composing the cycle index from some building blocks. However, those building blocks are also well explained and finally presented in a very detailed fashion.

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