Search results for "Mathematics::Group Theory"
showing 10 items of 174 documents
ON A PERMUTABILITY PROPERTY OF SUBGROUPS OF FINITE SOLUBLE GROUPS
2010
The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.
Sylow permutable subnormal subgroups of finite groups
2002
[EN] An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgroup is permutable and Sylow permutable.
Maximal subgroups of small index of finite almost simple groups
2022
We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\operatorname{l}(S)^2}$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by $\log^3 {\operatorname{l}(S)}$ and $\operatorname{l}(S)^2 < |S|$.
Some subgroup embeddings in finite groups: A mini review
2015
[EN] In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied. ª 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University
Commensurability classification of a family of right-angled Coxeter groups
2008
We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.
2-Groups with few rational conjugacy classes
2011
Abstract In this paper we prove the following conjecture of G. Navarro: if G is a finite 2-group with exactly 5 rational conjugacy classes, then G is dihedral, semidihedral or generalized quaternion. We also characterize the 2-groups with 4 rational classes.
Some problems about products of conjugacy classes in finite groups
2020
[EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.
Conjugacy problem for braid groups and Garside groups
2003
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
Root-restricted Kleenean rotations
2010
We generalize the Kleene theorem to the case where nonassociative products are used. For this purpose, we apply rotations restricted to the root of binary trees.
Invariant characters and coprime actions on finite nilpotent groups
2000
Suppose that a group A acts via automorphisms on a nilpotent group G having coprime order. Given an A-invariant character \(\chi \in {\rm Irr}(G)\), we show that the A-primitive irreducible characters that induce \(\chi \) from an A-invariant subgroup of G all have equal degree. We use this result to obtain some information about the characters of groups of p-length 1.