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pro vyhledávání: '"Khanh, Huynh Viet"'
In this paper, we study the torsion subgroup, which is denoted by ${\rm TK}_1(E)$, of the Whitehead group $E^*/[E^*,E^*]$ of a graded division algebra $E$ which is finite dimensional over its center. In particular, we provide formulas for ${\rm TK}_1
Externí odkaz:
http://arxiv.org/abs/2404.06801
In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with respect to
Externí odkaz:
http://arxiv.org/abs/2403.08595
Autor:
Hai, Bui Xuan, Khanh, Huynh Viet
In this paper, we prove that the multiplicative group of a unital non-commutative Leavitt path algebra $L_K(E)$ and Cohn path algebra $C_K(E)$ contain a non-cyclic free subgroup, provided $K$ is a non-absolute field. We also provide a description of
Externí odkaz:
http://arxiv.org/abs/2303.10744
Autor:
Hai, Bui Xuan, Khanh, Huynh Viet
The description of the subgroup structure of a non-commutative division ring is the subject of the intensive study in the theory of division rings in particular, and of the theory of skew linear groups in general. This study is still so far to be com
Externí odkaz:
http://arxiv.org/abs/2011.01905
Autor:
Khanh, Huynh Viet, Hai, Bui Xuan
Publikováno v:
Kyoto J. Math. 64(1): 245-260 (February 2024)
Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over $F$. Moreov
Externí odkaz:
http://arxiv.org/abs/1908.04925
Autor:
Danh, Le Qui, Khanh, Huynh Viet
Publikováno v:
Hiroshima Mathematical Journal, 2021
Let $D$ be a division ring with center $F$, and $G$ a subnormal or quasinormal subgroup of $D^*$. We show that if $G$ is locally solvable, then $G$ is contained in $F$.
Externí odkaz:
http://arxiv.org/abs/1903.11216
Autor:
Khanh, Huynh Viet, Hai, Bui Xuan
Publikováno v:
Publicacions Matem\`atiques (2022)
This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group $\GL_n(D)$ over a division ring $D$. It turns out that in the case where $D$ is non-commutative, if
Externí odkaz:
http://arxiv.org/abs/1903.10868
Autor:
Khanh, Huynh Viet
Publikováno v:
Journal of Algebra, 2019
Let $D$ be a division ring with center $F$, and $G$ a subnormal subgroup of $D^*$. We show that if $G$ is a locally solvable group such that $G^{(i)}$ is algebraic over $F$, then $G$ must be central. Also, if $M$ is non-abelian locally solvable maxim
Externí odkaz:
http://arxiv.org/abs/1810.07090
Autor:
Khanh, Huynh Viet, Hai, Bui Xuan
Let $D$ be a non-commutative division ring, $G$ a subnormal subgroup of ${\mathrm GL}_n(D)$. In this note we show that if $G$ contains a non-abelian solvable maximal subgroup, then $n=1$ and $D$ is a cyclic algebra of prime degree over $F$.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/1809.00356
Autor:
Hai, Bui Xuan, Khanh, Huynh Viet
Publikováno v:
International Journal of Algebra and Computation, 2019
The study of the existence of free groups in skew linear groups have been begun since the last decades of the 20-th century. The starting point is the theorem of Tits (1972), now often is referred as Tits' Alternative, stating that every finitely gen
Externí odkaz:
http://arxiv.org/abs/1808.08453