Minimal Number of Generators and Minimum Order of a Non-Abelian Group Whose Elements Commute with Their Endomorphic Images

DOI10.1080/00927870801941903zbMath1156.20019arXiv0708.2280OpenAlexW2963785189MaRDI QIDQ3514827

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Publication date: 23 July 2008

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2280

zbMATH Keywords

finite \(p\)-groupsnear-rings2-Engel groupsendomorphisms of groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Automorphisms of abstract finite groups (20D45) Automorphisms of infinite groups (20E36) Finite nilpotent groups, (p)-groups (20D15) Engel conditions (20F45)

Related Items (3)

3-Generator Groups Whose Elements Commute with Their Endomorphic Images Are Abelian ⋮ Direct product of four classes of groups. ⋮ Finite 3-groups of class 3 whose elements commute with their automorphic images.

Uses Software

• GAP

Cites Work

• Finite p-groups of exponent \(p^ 2\) in which each element commutes with its endomorphic images
• A non-abelian 2-group whose endomorphisms generate a ring, and other examples of E-groups
• On the minimal number of generators of finite non-abelian p-groups having an abelian automorphism group
• Unnamed Item

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