✦ LIBER ✦

Enumerating Boundedly Generated Finite Groups

✍ Scribed by Alexander Lubotzky

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 66 KB
Volume: 238
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8650

No coin nor oath required. For personal study only.

✦ Synopsis

We prove a conjecture of Mann and Pyber which estimates the number of finite groups of a given order and a given number of generators. This implies that the normal subgroup growth of free groups is of rate n log n .

📜 SIMILAR VOLUMES

Random Generation of Finite Simple Group

Random Generation of Finite Simple Groups

✍ Robert M. Guralnick; Martin W. Liebeck; Jan Saxl; Aner Shalev 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 88 KB

Probabilistic Generation of Finite Simpl

Probabilistic Generation of Finite Simple Groups

✍ Robert M. Guralnick; William M. Kantor 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 325 KB

For each finite simple group G there is a conjugacy class C such that each G nontrivial element of G generates G together with any of more than 1r10 of the members of C . Precise asymptotic results are obtained for the probability implicit G in this assertion. Similar results are obtained for almost

Ideals of Generalized Finite Sets in Lat

Ideals of Generalized Finite Sets in Lattices of α-Recursively Enumerable Sets

✍ Manuel Lerman 📂 Article 📅 1976 🏛 John Wiley and Sons 🌐 English ⚖ 444 KB

Algorithmic Methods for Finitely Generat

Algorithmic Methods for Finitely Generated Abelian Groups

✍ Henri Cohen; Francisco Diaz Y Diaz; Michel Olivier 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 357 KB

We describe algorithmic tools to compute with exact sequences of Abelian groups. Although simple in nature, these are essential for a number of applications such as the determination of the structure of (Z K /m) \* for an ideal m of a number field K, of ray class groups of number fields, and of cond

Combinatorial Classification of Finitely

Combinatorial Classification of Finitely Generated Virtually Free Groups

✍ Thomas Müller 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 203 KB

Digraphical Regular Representations of I

Digraphical Regular Representations of Infinite Finitely Generated Groups

✍ R.G. Möller; N. Seifter 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 104 KB

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infinite cyclic group Z. We show that a directed Cayley graph X (Z, S) is a DRR of Z if and only if As a general r