Premium
On the Fitting height of a soluble group that is generated by a conjugacy class of 3‐elements
Author(s) -
AlRoqi Abdullah,
Flavell Paul
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm102
Subject(s) - conjugacy class , mathematics , order (exchange) , prime (order theory) , group (periodic table) , class (philosophy) , combinatorics , element (criminal law) , pure mathematics , chemistry , organic chemistry , finance , artificial intelligence , computer science , political science , law , economics
Let G be a finite soluble group that is generated by a conjugacy class consisting of elements of order 3. We show that there exist four conjugates of an element of order 3 that generate a subgroup with the same Fitting height as G . We use this result to find a soluble analogue of the Baer–Suzuki theorem in the case prime 3.