math.GR · 2026-08-10 · No. 80

Group Theory, 2026-08-10.

1 new papers in math.GR. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

1 entries
  1. 01

    A Finite E-Group of Nilpotency Class Three

    Xinan Dai, Wenhao Deng, Yidong Shi, Tailin Wu, Yuchen Yang

    math.GR · cs.AI

    A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the $3$-group of order $3^{84}$ introduced by Abdollahi, Faghihi, and Mohammadi Hassanabadi, and later shown by Abdollahi, Faghihi, Linton, and O'Brien to have the corresponding automorphism property, is an E-group. Let $P$ denote this group and put $V=P/Φ(P)\cong...

    arxiv.org/abs/2608.07275 · PDF

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