AbstractLetting G(n) denote the number of nonisomorphic groups of order n, it is shown that for square-free n, G(n) ≤ ϕ(n) and G(n) ≤ (log n)c on a set of positive density. Letting Fk(x) denote the number of n ≤ x for which G(n) = k, it is shown that F2(x) = O(x(log4x)(log3x)2), where logrx denotes the r-fold iterated logarithm
Hölder\u27s formula for the number of groups of a square-free order is an early advance in the enu...
We prove that for every ϵ > 0 there exists a δ > 0 such that every group of order n ≥ 3 has at least...
Abstract. For any group G, pie(G) denotes the set of orders of its elements. If Ω is a non-empty sub...
AbstractLetting G(n) denote the number of nonisomorphic groups of order n, it is shown that for squa...
Let B be a subset of the set of all isomorphism classes of finite groups. We consider the number Fg(...
AbstractLet T be a subset of the set of all isomorphism classes of finite groups. We consider the nu...
AbstractLet a(n) denote the number of nonisomorphic Abelian groups with n elements. Several problems...
AbstractLet A denote the set of all natural numbers n such that every group of order n is Abelian. L...
The unsolved problem of whether there exists a positive constant c such that the number k(G) of conj...
AbstractFor any positive integer N, there are a finite number of non-isomorphic groups of order N. T...
The thesis centres around two problems in the enumeration of p-groups. Define fφ(pm) to be the numb...
AbstractLet |G| be the number of vertices of a graph G, let ω(G) be the density of G, and K(G) be th...
1.) Let d(n) denote the number of divisors of n, logkn the k-fold iterated logarithm. It was shown b...
AbstractLet N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=lim...
AbstractWe prove a conjecture of Mann and Pyber which estimates the number of finite groups of a giv...
Hölder\u27s formula for the number of groups of a square-free order is an early advance in the enu...
We prove that for every ϵ > 0 there exists a δ > 0 such that every group of order n ≥ 3 has at least...
Abstract. For any group G, pie(G) denotes the set of orders of its elements. If Ω is a non-empty sub...
AbstractLetting G(n) denote the number of nonisomorphic groups of order n, it is shown that for squa...
Let B be a subset of the set of all isomorphism classes of finite groups. We consider the number Fg(...
AbstractLet T be a subset of the set of all isomorphism classes of finite groups. We consider the nu...
AbstractLet a(n) denote the number of nonisomorphic Abelian groups with n elements. Several problems...
AbstractLet A denote the set of all natural numbers n such that every group of order n is Abelian. L...
The unsolved problem of whether there exists a positive constant c such that the number k(G) of conj...
AbstractFor any positive integer N, there are a finite number of non-isomorphic groups of order N. T...
The thesis centres around two problems in the enumeration of p-groups. Define fφ(pm) to be the numb...
AbstractLet |G| be the number of vertices of a graph G, let ω(G) be the density of G, and K(G) be th...
1.) Let d(n) denote the number of divisors of n, logkn the k-fold iterated logarithm. It was shown b...
AbstractLet N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=lim...
AbstractWe prove a conjecture of Mann and Pyber which estimates the number of finite groups of a giv...
Hölder\u27s formula for the number of groups of a square-free order is an early advance in the enu...
We prove that for every ϵ > 0 there exists a δ > 0 such that every group of order n ≥ 3 has at least...
Abstract. For any group G, pie(G) denotes the set of orders of its elements. If Ω is a non-empty sub...
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