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
Finite Groups With Many Conjugate Elements
โ Scribed by J.P. Zhang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 710 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0021-8693
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โฆ 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
๐ SIMILAR VOLUMES
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
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