On groups of even orders with automorphisms generating recurrent sequences of the maximal period
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Aleksandr V. Akishin
Abstract
Let G be a finite group and f be an automorphism of the group G. The automorphism f specifies a recurrent sequence {ai}0∞ on the group G by the rule ai+1 = f(ai). If a0 is the initial element of the sequence, then the period of the sequence does not exceed the number of elements having the same order as a0. Thus, it is interesting to find out whether there exist groups having automorphisms generating sequences with the largest possible period for any initial element. This work continues the study of groups possessing automorphisms of the maximal period. Earlier, the case of groups of odd orders was examined. It was established that such groups are necessarily Abelian, and their structure was completely described. This paper considers groups of even orders and completes the description of finite groups possessing automorphisms of the maximal period.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- On groups of even orders with automorphisms generating recurrent sequences of the maximal period
- Local contractivity of the process of a player rating variation in the Elo model with one adversary
- On regular hypergraphs with high girth and high chromatic number
- On repetitions of long tuples in a Markov chain
- Automorphism-extendable modules
- On read-once transformations of random variables over finite fields
Articles in the same Issue
- Frontmatter
- On groups of even orders with automorphisms generating recurrent sequences of the maximal period
- Local contractivity of the process of a player rating variation in the Elo model with one adversary
- On regular hypergraphs with high girth and high chromatic number
- On repetitions of long tuples in a Markov chain
- Automorphism-extendable modules
- On read-once transformations of random variables over finite fields
