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pro vyhledávání: '"Tsang, Cindy"'
Autor:
Tsang, Cindy
By previous work of Ced\'{o}, Smoktunowicz, and Vendramin, one already knows that the analog of Gr\"{u}n's lemma fails to hold for perfect skew left braces when the socle is used as an analog of the center of a group. In this paper, we use the annihi
Externí odkaz:
http://arxiv.org/abs/2409.18410
Autor:
Entin, Alexei, Tsang, Cindy
Publikováno v:
J. Pure Appl. Algebra 229 (2025), no. 1, Paper No. 107839, 11 pp
We show that every finite group $T$ is isomorphic to a normalizer quotient $N_{S_n}(H)/H$ for some $n$ and a subgroup $H\leq S_n$. We show that this holds for all large enough $n\ge n_0(T)$ and also with $S_n$ replaced by $A_n$. The two main ingredie
Externí odkaz:
http://arxiv.org/abs/2408.07133
Autor:
Stefanello, Lorenzo, Tsang, Cindy
Publikováno v:
J. Algebra 664 (2025), part A, 514-526
Let $L/K$ be any finite Galois extension with Galois group $G$. It is known by Chase and Sweedler that the Hopf--Galois correspondence is injective for every Hopf--Galois structure on $L/K$, but it need not be bijective in general. Hopf--Galois struc
Externí odkaz:
http://arxiv.org/abs/2406.15800
Autor:
Kozakai, Yuta, Tsang, Cindy
Publikováno v:
Int. J. Group Theory 14 (2025), no. 3, 149-164
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility condition. Foll
Externí odkaz:
http://arxiv.org/abs/2405.08662
Autor:
Tsang, Cindy
In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In particular, our
Externí odkaz:
http://arxiv.org/abs/2312.15745
Autor:
Tsang, Cindy
Publikováno v:
J. Algebra 642 (2024), 367-399
The famous theorem of It\^{o} in group theory states that if a group $G=HK$ is the product of two abelian subgroups $H$ and $K$, then $G$ is metabelian. We shall generalize this to the setting of a skew brace $(A,{\cdot\,},\circ)$. Our main result sa
Externí odkaz:
http://arxiv.org/abs/2305.10081
Autor:
Caranti, A., Tsang, Cindy
Publikováno v:
J. Group Theory 27 (2024), no. 2, 345-381
We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order $p^{r-1}(p-1)$, w
Externí odkaz:
http://arxiv.org/abs/2303.10638
Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension
Autor:
Tsang, Cindy
Publikováno v:
Bull. Lond. Math. Soc. 55 (2023), no.5, 2324-2340
We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of skew braces, our result gives a complete list of finite non-abelian simple groups which occur as the addi
Externí odkaz:
http://arxiv.org/abs/2210.14689
Autor:
Caranti, A., Tsang, Cindy
Publikováno v:
J. Algebra 617 (2023), 476-499
Let $G$ be any group. The quotient group $T(G)$ of the multiple holomorph by the holomorph of $G$ has been investigated for various families of groups $G$. In this paper, we shall take $G$ to be a finite $p$-group of class two for any odd prime $p$,
Externí odkaz:
http://arxiv.org/abs/2205.15205
Autor:
Stefanello, Lorenzo, Tsang, Cindy
Publikováno v:
In Journal of Algebra 15 February 2025 664 Part A:514-526
