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The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.

Non-nilpotent subgroups of locally graded groups

Mohammad Zarrin (2015)

Colloquium Mathematicae

We show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log₂n] + m + 3)-by-(finite of order ≤ m!). We also show that the derived length of a soluble group with a finite number m of non-(nilpotent of class at most n) subgroups is at most [log₂ n] + m + 1.

Normal Subgroup of Product of Groups

Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama (2011)

Formalized Mathematics

In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.

Normal subgroups of classical groups over Banach algebras.

Leonid N. Vaserstein (1988)

Commentarii mathematici Helvetici

Normal Subgroups of N.E.C. Groups.

Emilio Bujalance (1981)

Mathematische Zeitschrift

Normalizers and self-normalizing subgroups II

Boris Širola (2011)

Open Mathematics

Let $𝕂$ be a field, G a reductive algebraic $𝕂$ -group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of $𝕂$ -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, $𝕂$ ) in G = SL(m, $𝕂$ ) we have N ≅ G 1 ⋊ µm( $𝕂$ ), the semidirect product of G 1 by the group of m-th roots of unity in $𝕂$ . The normalizers of the even orthogonal and symplectic subgroup of SL(2n, $𝕂$ ) were computed in [Širola B., Normalizers and self-normalizing...

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Nets associated with the elementary nets.

Neuer Beweis eines Fundamentaltheorems aus der Theorie der Substitutionslehre

Nielsen methods in groups with a length function.

Nielsen reduction in free groups with operators

Nilpotent Groups of Hirsch Length Six.

Non-amenable finitely presented torsion-by-cyclic groups

Non-free two-generator subgroups of SL2(Q).

Non-nilpotent subgroups of locally graded groups

Normal Subgroup of Product of Groups

Normal subgroups of classical groups over Banach algebras.

Normal Subgroups of N.E.C. Groups.

Normalizers and self-normalizing subgroups II

On a class of groups with strongly embedded subgroup.

On a class of residually finite groups.

On a generalization of groups with all subgroups subnormal

On a generalization of the Baer-Suzuki theorem.

On a New Characterization of Demuskin Groups.

On a problem on explicit embeddings of the group $ℚ$ .

On a property of groups with coverings.

On a question of Deaconescu about automorphisms. - III

Currently displaying 161 – 180 of 544