On groups 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} on the group G, i = 0, 1, . . ., according to the rule ai+1 = f(ai). If a0 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 a0. 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.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- On groups with automorphisms generating recurrent sequences of the maximal period
- Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
- Free commutative medial n-ary groupoids
- Complexity of implementation of parity functions in the implication–negation basis
- Closed classed of three-valued logic that contain essentially multiplace functions
- A generalization of Ore’s theorem on irreducible polynomials over a finite field
- Rings whose finitely generated right ideals are quasi-projective
Articles in the same Issue
- Frontmatter
- On groups with automorphisms generating recurrent sequences of the maximal period
- Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
- Free commutative medial n-ary groupoids
- Complexity of implementation of parity functions in the implication–negation basis
- Closed classed of three-valued logic that contain essentially multiplace functions
- A generalization of Ore’s theorem on irreducible polynomials over a finite field
- Rings whose finitely generated right ideals are quasi-projective
