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Noncyclic graph of a group
, 2007
"... We associate a graph ΓG to a non locally cyclic group G (called the noncyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G  〈x, y 〉 is cyclic for all y ∈ G}, and join two vertices if they do not generate a cyclic subgroup. We study the properties of this graph and ..."
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We associate a graph ΓG to a non locally cyclic group G (called the noncyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G  〈x, y 〉 is cyclic for all y ∈ G}, and join two vertices if they do not generate a cyclic subgroup. We study the properties of this graph
Noncyclic graph associated with a group
, 2008
"... We associate a graph CG to a non locally cyclic group G (called the noncyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G  〈x, y 〉 is cyclic for all y ∈ G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup. For a simple ..."
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We associate a graph CG to a non locally cyclic group G (called the noncyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G  〈x, y 〉 is cyclic for all y ∈ G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup. For a simple
and
, 2005
"... Let H be a subgroup of a group G. We say that H satisfies the power condition with respect to G, or H is a power subgroup of G, if there exists a nonnegative integer m such that H = G m =< g m g ∈ G>. In this note, the following theorem is proved: Let G be a group and k the number of nonpow ..."
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power subgroups of G. Then (1) k = 0 if and only if G is a cyclic group(theorem of F. Szász);(2) 0 < k < ∞ if and only if G is a finite noncyclic group; (3) k = ∞ if and only if G is a infinte noncyclic group. Thus we get a new criterion for the finite noncyclic groups.
www.ui.ac.ir COVERING MONOLITHIC GROUPS WITH PROPER SUBGROUPS
"... Abstract. Given a finite noncyclic group G, call σ(G) the smallest number of proper subgroups of G needed to cover G. Lucchini and Detomi conjectured that if a nonabelian group G is such that σ(G) < σ(G/N) for every nontrivial normal subgroup N of G then G is monolithic, meaning that it admits ..."
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Abstract. Given a finite noncyclic group G, call σ(G) the smallest number of proper subgroups of G needed to cover G. Lucchini and Detomi conjectured that if a nonabelian group G is such that σ(G) < σ(G/N) for every nontrivial normal subgroup N of G then G is monolithic, meaning that it admits
Facultad de Ciencias, Universidad Central de Venezuela
"... A theorem by Caro states that every sequence of elements in an abelian non cyclic group of order n, not of the form Z2 ⊕ Z2m, with length 4n3 + 1 contains an nsubsequence (subsequence of length n) with a zerosum. In this paper, we obtain a more precise result by showing that in an abelian non cycl ..."
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A theorem by Caro states that every sequence of elements in an abelian non cyclic group of order n, not of the form Z2 ⊕ Z2m, with length 4n3 + 1 contains an nsubsequence (subsequence of length n) with a zerosum. In this paper, we obtain a more precise result by showing that in an abelian non
IRREDUCIBLE 4MANIFOLDS WITH ABELIAN NONCYCLIC FUNDAMENTAL GROUP OF SMALL RANK
, 903
"... In this paper we construct several irreducible 4manifolds, both small and arbitrarily large, with abelian noncyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the geography plane of symplectic manifolds with π1 = Z ⊕ Z, Z ⊕ Zp and Zq ⊕ Zp (gcd(p, q) ̸ = ..."
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In this paper we construct several irreducible 4manifolds, both small and arbitrarily large, with abelian noncyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the geography plane of symplectic manifolds with π1 = Z ⊕ Z, Z ⊕ Zp and Zq ⊕ Zp (gcd(p, q) ̸
SMALL IRREDUCIBLE SYMPLECTIC 4MANIFOLDS WITH ABELIAN NONCYCLIC FUNDAMENTAL GROUP
, 903
"... In this paper we construct several small irreducible symplectic 4manifolds with abelian noncyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the Geography plane of symplectic manifolds with π1 = Z ⊕ Zp and π1 = Zq ⊕ Zp (gcd(p, q) ̸ = 1). The main result ..."
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In this paper we construct several small irreducible symplectic 4manifolds with abelian noncyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the Geography plane of symplectic manifolds with π1 = Z ⊕ Zp and π1 = Zq ⊕ Zp (gcd(p, q) ̸ = 1). The main result
FINITE GROUPS WITH THREE RELATIVE COMMUTATIVITY DEGREES
"... Abstract. For a finite group G and a subgroup H of G, the relative commutativity degree of H in G, denoted by d(H,G), is the probability that an element of H commutes with an element of G. Let D(G) = {d(H,G) : H ≤ G} be the set of all relative commutativity degrees of subgroups of G. It is shown ..."
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that a finite group G admits three relative commutativity degrees if and only if G/Z(G) is a noncyclic group of order pq, where p and q are primes. Moreover, we determine all the relative commutativity degrees of some known groups. 1.
Wedderburn decomposition of finite group algebras
"... We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelianbysupersolvable group G from certain pairs of subgroups of G. In this paper F = Fq denotes a finite field with q elements and G is a finite g ..."
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of cyclic groups [10]. More generally, there is a long tradition on the study of abelian codes (ideals in finite abelian group algebras) or group codes (one sided ideals in arbitrary finite group algebras) [1, 2, 3, 5, 6, 11, 13, 14, 15]. One of the major motivations in the study of non cyclic group algebra
Results 1  10
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679