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articleNo Access
A Note on TI-Subgroups of a Finite Group
- Jiangtao Shi and
- Cui Zhang
Algebra Colloquium11 Apr 2014
Preview Abstract
Let G be a finite group and H a subgroup of G. Recall that H is said to be a TI-subgroup of G if H^g∩ H = 1 or H for each g ∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G are TI-subgroups, then G is soluble, and all non-nilpotent subgroups of G are normal.
articleNo Access
Automorphism Groups of a Class of Cubic Cayley Graphs on Symmetric Groups
- Xueyi Huang,
- Qiongxiang Huang, and
- Lu Lu
Algebra Colloquium15 Nov 2017
Preview Abstract
Let S_n denote the symmetric group of degree n with n ≥ 3, S = { c_n = (1 2 ⋯ n), $c_{n}^{- 1}$ $c_{n}^{- 1}$ , (1 2)} and Γ_n = Cay(S_n, S) be the Cayley graph on S_n with respect to S. In this paper, we show that Γ_n (n ≥ 13) is a normal Cayley graph, and that the full automorphism group of Γ_n is equal to Aut(Γ_n) = R(S_n) ⋊ 〈Inn(ϕ) ≅ S_n × ℤ₂, where R(S_n) is the right regular representation of S_n, ϕ = (1 2)(3 n)(4 n−1)(5 n−2) ⋯ (∊ S_n), and Inn(ϕ) is the inner isomorphism of S_n induced by ϕ.

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