๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Finite Groups With Many Conjugate Elements

โœ Scribed by J.P. Zhang


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
710 KB
Volume
170
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis


In this paper we prove the following long-standing conjecture in the theory of finite groups: Finite solvable groups with no two distinct conjugacy classes of the same length are isomorphic to the symmetric group of degree 3. r 1994 Academic Press. Inc


๐Ÿ“œ SIMILAR VOLUMES


Finite Groups Containing Many Subgroups
โœ Marcel Herzog; Patrizia Longobardi; Mercede Maj; Avinoam Mann ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 160 KB

In this paper G denotes a finite group. As is well known, the converse of Lagrange's theorem in group theory does not hold. That is, given a finite group G of order n, and given a divisor d of n, G need not have a subgroup of order d. Indeed, a celebrated theorem of P. Hall states that it suffices t

Generating Finite Groups with Conjugates
โœ Paul Flavell ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 298 KB

Suppose that H is a subgroup of a finite group G and that G is generated by the conjugates of H. In this paper, we consider the following question: when can G be generated by two conjugates of H? We began the study of this question in [2]. In order to discuss the results proved in [2] and in this p

Groups with Many FC-Subgroups
โœ Silvana Franciosi; Francesco de Giovanni; Yaroslav P. Sysak ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 120 KB

DEDICATED TO DEREK J. S. ROBINSON ON THE OCCASION OF HIS 60TH BIRTHDAY ## 1. Introduction A group G is called an FC-group if every element x of G has only ลฝ . finitely many conjugates in G, that is, if the centralizer C x has finite G index in G. There exists a wide literature on this subject, and