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CROSSED PRODUCT OF CYCLIC GROUPS
, 809
"... Abstract. All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given. ..."
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Cited by 1 (1 self)
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Abstract. All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
ON GENERIC POLYNOMIALS FOR CYCLIC GROUPS
"... Abstract. Starting from a known case of generic polynomials for dihedral groups, we get a family of generic polynomials for cyclic groups of order divisible by four over suitable base fields. 1. ..."
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Abstract. Starting from a known case of generic polynomials for dihedral groups, we get a family of generic polynomials for cyclic groups of order divisible by four over suitable base fields. 1.
THE LINDLEHMER CONSTANT FOR CYCLIC GROUPS OF
"... Abstract. We determine the Lind Lehmer constant for the cyclic group Zn ..."
PERMUTATIONS OVER CYCLIC GROUPS
"... Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements a1,..., am of the cyclic group of order m, there is a permutation pi such that 1a pi(1) + · · ·+mapi(m) = 0. ..."
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Cited by 1 (1 self)
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Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements a1,..., am of the cyclic group of order m, there is a permutation pi such that 1a pi(1) + · · ·+mapi(m) = 0.
Cyclic groups and knapsack facets
 MATH. PROGRAM., SER. B 96: 377–408 (2003)
, 2003
"... Any integer program may be relaxed to a group problem. We define the master cyclic group problem and several master knapsack problems, show the relationship between the problems, and give several classes of facetdefining inequalities for each problem, as well as a set of mappings that take facets ..."
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Cited by 15 (0 self)
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Any integer program may be relaxed to a group problem. We define the master cyclic group problem and several master knapsack problems, show the relationship between the problems, and give several classes of facetdefining inequalities for each problem, as well as a set of mappings that take facets
ON THE ESSENTIAL DIMENSION OF CYCLIC GROUPS
"... Abstract. We find an upper bound for the essential dimension of finite cyclic groups Z/p n1 1 ···pnr r Z over a field F of characteristic different from pi containing all the primitive pith roots of unity, where pi are distinct prime numbers. 1. ..."
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Abstract. We find an upper bound for the essential dimension of finite cyclic groups Z/p n1 1 ···pnr r Z over a field F of characteristic different from pi containing all the primitive pith roots of unity, where pi are distinct prime numbers. 1.
Average Order in Cyclic Groups
, 2002
"... For each natural number n we determine the average order #(n) of the elements in a cyclic group of order n. We show that a large fraction of the contribution to #(n) comes from the #(n) primitive elements of order n. It is therefore of interest to study also the function #(n) = #(n)/#(n). We determi ..."
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Cited by 6 (1 self)
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For each natural number n we determine the average order #(n) of the elements in a cyclic group of order n. We show that a large fraction of the contribution to #(n) comes from the #(n) primitive elements of order n. It is therefore of interest to study also the function #(n) = #(n)/#(n). We
Permutation Polytopes of Cyclic Groups
, 2012
"... We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial desc ..."
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Cited by 2 (2 self)
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We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial
Average Order in Cyclic Groups
 JOURNAL DE THÉORIE DES NOMBRES
, 2004
"... For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We determi ..."
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For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We
Chirps on finite cyclic groups
"... Chirps arise in many signal processing applications, and have been extensively studied, especially in the case where chirps are regarded as functions of the realline or of the integers. However, less attention has been paid to study of chirps over finite cyclic groups. We discuss the basic properti ..."
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Chirps arise in many signal processing applications, and have been extensively studied, especially in the case where chirps are regarded as functions of the realline or of the integers. However, less attention has been paid to study of chirps over finite cyclic groups. We discuss the basic
Results 1  10
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4,328