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On automorphisms fixing subnormal subgroups of soluble groups

Silvana Franciosi, Francesco de Giovanni (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The group A u t s n G of all automorphisms leaving invariant every subnormal subgroup of the group G is studied. In particular it is proved that A u t s n G is metabelian if G is soluble, and that A u t s n G is either finite or abelian if G is polycyclic.

On centrally nilpotent loops

L. V. Safonova, K. K. Shchukin (2000)

Commentationes Mathematicae Universitatis Carolinae

Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

On computing quaternion quotient graphs for function fields

Gebhard Böckle, Ralf Butenuth (2012)

Journal de Théorie des Nombres de Bordeaux

Let Λ be a maximal 𝔽 q [ T ] -order in a division quaternion algebra over 𝔽 q ( T ) which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units Λ * on the Bruhat-Tits tree 𝒯 associated to PGL 2 ( 𝔽 q ( ( 1 / T ) ) ) . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group Λ * in terms of generators and relations. Moreover we determine an upper bound...

On congruence permutable G -sets

Attila Nagy (2020)

Commentationes Mathematicae Universitatis Carolinae

An algebraic structure is said to be congruence permutable if its arbitrary congruences α and β satisfy the equation α β = β α , where denotes the usual composition of binary relations. To an arbitrary G -set X satisfying G X = , we assign a semigroup ( G , X , 0 ) on the base set G X { 0 } containing a zero element 0 G X , and examine the connection between the congruence permutability of the G -set X and the semigroup ( G , X , 0 ) .

On connectedness of graphs on direct product of Weyl groups

Samy A. Youssef, S. G. Hulsurkar (1995)

Archivum Mathematicum

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.

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