On the Fitting height of a soluble group that is generated by a conjugacy class of 3‐elements | Zendy

AlRoqi Abdullah | Zendy; Flavell Paul | Zendy

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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.

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