Finite groups satisfying the independence property
Date
01/05/2023Metadata
Show full item recordAbstract
We say that a finite group G satisfies the independence property if, for every pair of distinct elements x and y of G, either {x, y} is contained in a minimal generating set for G or one of x and y is a power of the other. We give a complete classification of the finite groups with this property, and in particular prove that every such group is supersoluble. A key ingredient of our proof is a theorem showing that all but three finite almost simple groups H contain an element s such that the maximal subgroups of H containing s, but not containing the socle of H, are pairwise non-conjugate.
Citation
Freedman , S D , Lucchini , A , Nemmi , D & Roney-Dougal , C M 2023 , ' Finite groups satisfying the independence property ' , International Journal of Algebra and Computation , vol. 33 , no. 3 , pp. 509-545 . https://doi.org/10.1142/S021819672350025X
Publication
International Journal of Algebra and Computation
Status
Peer reviewed
ISSN
0218-1967Type
Journal article
Description
Funding: The first author was supported by a St Leonard’s International Doctoral Fees Scholarship and a School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews. The fourth author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Groups, Representations and Applications: New perspectives”, where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1, and also partially supported by a grant from the Simons Foundation.Collections
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