Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Equivalent Expressions of Direct Sum Decomposition of Groups1

100%
Nakasho K., Okazaki H., Yamazaki H., Shidama Y.
Formalized Mathematics
|
2015
|
tom 23
|
nr 1
67-73
EN
In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.
2
Content available remote

The divisible radical of a group

100%
Wehrfritz B. A. F.
Open Mathematics
|
2009
|
tom 7
|
nr 3
387-394
EN
We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples than positive results. These counterexamples constitute the substantive part of this paper.
3
Content available remote

Definition and Properties of Direct Sum Decomposition of Groups1

100%
Nakasho K., Yamazaki H., Okazaki H., Shidama Y.
Formalized Mathematics
|
2015
|
tom 23
|
nr 1
15-27
EN
In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.
4
Content available remote

Normalizers and self-normalizing subgroups II

76%
Širola B.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1317-1332
EN
Let $\mathbb{K}$ be a field, G a reductive algebraic $\mathbb{K}$-group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of $\mathbb{K}$-points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, $\mathbb{K}$) in G = SL(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ µm($\mathbb{K}$), the semidirect product of G 1 by the group of m-th roots of unity in $\mathbb{K}$. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, $\mathbb{K}$) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = GL(m, $\mathbb{K}$) and G 1 = O(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ $\mathbb{K}$ ×. In both of these cases, N is a self-normalizing subgroup of G.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.