On finite groups with prescribed two-generator subgroups and integral Cayley graphs

2021/04/01 by Yan‐Quan Feng, Feng, Yan-Quan, István Kovács +1
Engineering · Mathematics · #20D45 #20E25 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2104.00434

openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we characterize the finite groups G of even order with the property that for any involution x and element y of G, ⟨ x, y ⟩ is isomorphic to one of the following groups: ℤ₂, ℤ₂², ℤ₄, ℤ₆, ℤ₂ × ℤ₄, ℤ₂ ×ℤ₆ and A₄. As a result, a characterization will be obtained for the finite groups all of whose Cayley graphs of degree 3 have integral spectrum.

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