Local conjugation in finite groups
โ Scribed by S.W Dolan
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 637 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The main result of the paper is the following theorem. Let G be a locally finite group containing a finite p-subgroup A such that C G A is finite and a non-cyclic subgroup B of order p 2 such that C G b has finite exponent for all b โ B # . Then G is almost locally solvable and has finite exponent.
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
But P l B s rad P and so L ( Prrad P. It remains to show that P F L . 1 2 If Q is a maximal normal subgroup of P then, since P is perfect, PrQ is isomorphic to a simple direct factor of L and hence has order greater 1 than s. With the notation as in Lemma 2.2, we have PE rE ( PrP l E , 2 2 2 which t