On subgroups containing non-trivial normal subgroups

Marcel Herzog*, Gil Kaplan, Andrea Lucchini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove that if A ≠ 1 is a subgroup of a finite group G and the order of an element in the centralizer of A in G is strictly larger (larger or equal) than the index [G:A], then A contains a non-trivial characteristic (normal) subgroup of G. Consequently, if A is a stabilizer in a transitive permutation group of degree m > 1, then exp (Z(A)) < m. These theorems generalize some recent results of Isaacs and the authors.

Original languageEnglish
Pages (from-to)183-188
Number of pages6
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Dec 2003


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