Geodesic
On groups with automorphisms generating recurrent sequences of the maximal period
Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 3-9

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a finite group and $f$ be an automorphism of the group $G$. The automorphism $f$ specifies a recurrent sequence $\{ a_i \}$ on the group $G$, $i = 0, 1, \ldots$, according to the rule $a_{i+1} = f(a_i)$. If $a_0$ is the initial element of the sequence, then its period does not exceed the number of elements in the group having the same order as the element $a_0$. Thus, it makes sense to formulate the question of whether there exist groups in which such recurrent sequence for a certain automorphism has the maximal period for any initial element. In this paper we introduce the notion of an automorphism of the maximal period and find all Abelian groups and finite groups of odd orders having automorphisms of the maximal period. Also, a number of results for finite groups of even orders are established.
Keywords: finite groups, regular automorphisms, recurrent sequences on groups. 
@article{DM_2014_26_1_a0,
     author = {A. V. Akishin},
     title = {On groups with automorphisms generating recurrent sequences of the maximal period},
     journal = {Diskretnaya Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2014_26_1_a0/}
}
TY  - JOUR
AU  - A. V. Akishin
TI  - On groups with automorphisms generating recurrent sequences of the maximal period
JO  - Diskretnaya Matematika
PY  - 2014
SP  - 3
EP  - 9
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2014_26_1_a0/
LA  - ru
ID  - DM_2014_26_1_a0
ER  - 
%0 Journal Article
%A A. V. Akishin
%T On groups with automorphisms generating recurrent sequences of the maximal period
%J Diskretnaya Matematika
%D 2014
%P 3-9
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2014_26_1_a0/
%G ru
%F DM_2014_26_1_a0
A. V. Akishin. On groups with automorphisms generating recurrent sequences of the maximal period. Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/DM_2014_26_1_a0/