Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type

Cheryl E. Praeger, Csaba Schneider

Research output: Contribution to journalArticle

3 Citations (Scopus)


We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product action. The proof uses several deep results that concern factorisations of direct products involving subdirect subgroups. We find that such factorisations are controlled by the existence of uniform automorphisms.

Original languageEnglish
Pages (from-to)1001-1023
JournalIsrael Journal of Mathematics
Issue number2
Publication statusPublished - Oct 2018


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