On parallelisms of PG(5, 2) invariant under a cyclic subgroup of order 21

2021 ◽  
Author(s):  
Svetlana Topalova ◽  
Stela Zhelezova
Keyword(s):  
Cyclic Subgroup

On locally graded barely transitive groups

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Cansu Betin ◽  
Mahmut Kuzucuoğlu
Keyword(s):  
Finite Index ◽  
Cyclic Subgroup ◽  
Transitive Group ◽  
Transitive Groups ◽  
Point Stabilizer

AbstractWe show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

scholarly journals Polygonal products of polycyclic by finite groups

1996 ◽  
Vol 54 (3) ◽  
pp. 369-372 ◽  
Author(s):  
R.B.J.T. Allenby
Keyword(s):  
Finite Groups ◽  
Cyclic Subgroup ◽  
Substantial Improvement ◽  
Normal Subgroups ◽  
Recent Theorem

We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.

scholarly journals On the finite $p$-groups with unique cyclic subgroup of given order

2016 ◽  
Vol 40 ◽  
pp. 244-249
Author(s):  
Libo ZHAO ◽  
Yangming LI ◽  
u L\" GONG
Keyword(s):  
Cyclic Subgroup

On the Morava K-theory of some finite 2-groups

1997 ◽  
Vol 121 (1) ◽  
pp. 7-13 ◽  
Author(s):  
BJÖRN SCHUSTER
Keyword(s):  
Finite Group ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Abelian Groups ◽  
Wreath Products ◽  
Classifying Space ◽  
Generalized Cohomology ◽  
K Theory ◽  
A Finite Group ◽  
Generalized Quaternion

For any fixed prime p and any non-negative integer n there is a 2(pn − 1)-periodic generalized cohomology theory K(n)*, the nth Morava K-theory. Let G be a finite group and BG its classifying space. For some time now it has been conjectured that K(n)*(BG) is concentrated in even dimensions. Standard transfer arguments show that a finite group enjoys this property whenever its p-Sylow subgroup does, so one is reduced to verifying the conjecture for p-groups. It is easy to see that it holds for abelian groups, and it has been proved for some non-abelian groups as well, namely groups of order p3 ([7]) and certain wreath products ([3], [2]). In this note we consider finite (non-abelian) 2-groups with maximal normal cyclic subgroup, i.e. dihedral, semidihedral, quasidihedral and generalized quaternion groups of order a power of two.

FINITE GROUPS WITH GIVEN NEARLY S-QUASINORMAL SUBGROUPS

2008 ◽  
Vol 01 (03) ◽  
pp. 369-382
Author(s):  
Nataliya V. Hutsko ◽  
Vladimir O. Lukyanenko ◽  
Alexander N. Skiba
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Saturated Formation ◽  
Supersoluble Groups ◽  
Sylow Subgroups ◽  
Quasinormal Subgroup ◽  
A Finite Group

Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-quasinormal in G. Then we say that H is nearly S-quasinormal in G if G has an S-quasinormal subgroup T such that HT = G and T ∩ H ≤ HsG. Our main result here is the following theorem. Let [Formula: see text] be a saturated formation containing all supersoluble groups and G a group with a normal subgroup E such that [Formula: see text]. Suppose that every non-cyclic Sylow subgroup P of E has a subgroup D such that 1 < |D| < |P| and all subgroups H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is a non-abelian 2-group) having no supersoluble supplement in G are nearly S-quasinormal in G. Then [Formula: see text].

A study of enhanced power graphs of finite groups

2019 ◽  
Vol 19 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Samir Zahirović ◽  
Ivica Bošnjak ◽  
Rozália Madarász
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Cyclic Subgroup ◽  
Nilpotent Groups ◽  
Sufficient Condition ◽  
Finite Abelian Groups ◽  
Power Graph ◽  
Vertex Set ◽  
A Finite Group

The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between undirected power graph of finite groups is an isomorphism between enhanced power graphs of these groups, and we find all finite groups [Formula: see text] for which [Formula: see text] is abelian, all finite groups [Formula: see text] with [Formula: see text] being prime power, and all finite groups [Formula: see text] with [Formula: see text] being square-free. Also, we describe enhanced power graphs of finite abelian groups. Finally, we give a characterization of finite nilpotent groups whose enhanced power graphs are perfect, and we present a sufficient condition for a finite group to have weakly perfect enhanced power graph.

A formula of subgroup normality degrees with applications to the finite p-groups with cyclic subgroups of index p2

2019 ◽  
Vol 19 (04) ◽  
pp. 2050073
Author(s):  
Mohammad Farrokhi D. G. ◽  
Yugen Takegahara
Keyword(s):  
Finite Group ◽  
Cyclic Subgroup ◽  
Index Formula ◽  
Cyclic Subgroups ◽  
A Finite Group

We give a formula for the subgroup normality degree [Formula: see text] of a subgroup [Formula: see text] in a finite group [Formula: see text], and determine subgroup normality degrees in the case where [Formula: see text] is a finite [Formula: see text]-group of order [Formula: see text] or a finite [Formula: see text]-group with a cyclic subgroup of index [Formula: see text].

When does a right-angled Artin group split over ℤ?

2014 ◽  
Vol 24 (06) ◽  
pp. 815-825 ◽  
Author(s):  
Matt Clay
Keyword(s):  
Cyclic Subgroup ◽  
Artin Group ◽  
Artin Groups ◽  
Cyclic Subgroups ◽  
Right Angled Artin Groups ◽  
Jsj Decompositions

We show that a right-angled Artin group, defined by a graph Γ that has at least three vertices, does not split over an infinite cyclic subgroup if and only if Γ is biconnected. Further, we compute JSJ-decompositions of 1-ended right-angled Artin groups over infinite cyclic subgroups.

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