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Central Camina pairs

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Abstract

Let (G, Z(G)) be a Camina pair. We prove that ∣G: Z(G)∣ > ∣Z(G)∣2 when G has nilpotence class at least 4. When G has nilpotence class 3, we show that ∣G: Z(G)∣ > ∣Z(G)∣3/2. Under the additional assumption that Z2(G) < CG(G′), the inequality ∣G: Z(G)∣≥ ∣Z(G)∣2∣G′: Z(G)∣ is established. If Z2(G) < CG(G′) and G has nilpotence class at least 4, then the inequality ∣G: Z(G)∣ > ∣Z(G)∣3 is obtained.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    David G. Costanzo & Mark L. Lewis

Authors
  1. David G. Costanzo
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  2. Mark L. Lewis
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Correspondence to David G. Costanzo.

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Costanzo, D.G., Lewis, M.L. Central Camina pairs. Isr. J. Math. 241, 991–1000 (2021). https://doi.org/10.1007/s11856-021-2122-4

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  • DOI: https://doi.org/10.1007/s11856-021-2122-4

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