scholarly journals Counting conjugacy classes of cyclic subgroups for fusion systems

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Sejong Park
Keyword(s):  
Finite Group ◽  
Conjugacy Classes ◽  
Cyclic Subgroups ◽  
Interesting Observation ◽  
Fusion Systems ◽  
A Finite Group

Abstract.Thévenaz [Arch. Math. (Basel) 52 (1989), no. 3, 209–211] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group

On Solvability of Groups with a Few Non-cyclic Subgroups

2016 ◽  
Vol 23 (01) ◽  
pp. 105-110 ◽  
Author(s):  
Mohammad Zarrin
Keyword(s):  
Finite Group ◽  
Sufficient Conditions ◽  
Study Groups ◽  
Conjugacy Classes ◽  
Cyclic Subgroups ◽  
A Finite Group

Li and Zhao studied groups with a few conjugacy classes of non-cyclic subgroups. In this paper we study groups with a few non-cyclic subgroups. In fact, among other things, we give some sufficient conditions on the number of non-cyclic subgroups of a finite group to be solvable.

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

scholarly journals On the Number of Conjugacy Classes of a Finite Group

1993 ◽  
Vol 160 (2) ◽  
pp. 441-460 ◽  
Author(s):  
L.G. Kovacs ◽  
G.R. Robinson
Keyword(s):  
Finite Group ◽  
Conjugacy Classes ◽  
A Finite Group

Conditions on the Edges and Vertices of Non-commuting Graph

2015 ◽  
Vol 74 (1) ◽  
Author(s):  
M. Jahandideh ◽  
M. R. Darafsheh ◽  
N. H. Sarmin ◽  
S. M. S. Omer
Keyword(s):  
Finite Group ◽  
Conjugacy Classes ◽  
Commuting Graph ◽  
Vertex Set ◽  
A Finite Group

Abstract - Let G􀡳 be a non- abelian finite group. The non-commuting graph ,􀪡is defined as a graph with a vertex set􀡳 − G-Z(G)􀢆in which two vertices x􀢞 and y􀢟 are joined if and only if xy􀢞􀢟 ≠ yx􀢟􀢞.  In this paper, we invest some results on the number of edges set , the degree of avertex of non-commuting graph and the number of conjugacy classes of a finite group. In order that if 􀪡􀡳non-commuting graph of H ≅ non - commuting graph of G􀪡􀡴,H 􀡴 is afinite group, then |G􀡳| = |H􀡴| .

On the number of conjugacy classes in a finite group II

1988 ◽  
Vol 64 (1) ◽  
pp. 87-127 ◽  
Author(s):  
Antonio Vera-López ◽  
MA Concepción Larrea
Keyword(s):  
Finite Group ◽  
Conjugacy Classes ◽  
Group Ii ◽  
A Finite Group

scholarly journals Duality for finite abelian hypergroups over splitting fields

1979 ◽  
Vol 20 (1) ◽  
pp. 57-70 ◽  
Author(s):  
J.R. McMullen ◽  
J.F. Price
Keyword(s):  
Finite Group ◽  
Duality Theory ◽  
Abelian Groups ◽  
Conjugacy Classes ◽  
Finite Abelian Groups ◽  
Precise Sense ◽  
Classical Duality ◽  
A Finite Group

A duality theory for finite abelian hypergroups over fairly general fields is presented, which extends the classical duality for finite abelian groups. In this precise sense the set of conjugacy classes and the set of characters of a finite group are dual as hypergroups.

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].

THE NUMBER OF CONJUGACY CLASSES CONTAINED IN NORMAL SUBGROUPS OF SOLVABLE GROUPS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250204
Author(s):  
AMIN SAEIDI ◽  
SEIRAN ZANDI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Solvable Groups ◽  
Conjugacy Classes ◽  
Normal Subgroups ◽  
A Finite Group

Let G be a finite group and let N be a normal subgroup of G. Assume that N is the union of ξ(N) distinct conjugacy classes of G. In this paper, we classify solvable groups G in which the set [Formula: see text] has at most three elements. We also compute the set [Formula: see text] in most cases.

scholarly journals Bounding the number of classes of a finite group in terms of a prime

2020 ◽  
Vol 23 (3) ◽  
pp. 471-488 ◽  
Author(s):  
Attila Maróti ◽  
Iulian I. Simion
Keyword(s):  
Finite Group ◽  
Conjugacy Classes ◽  
A Finite Group ◽  
Number Of Classes

AbstractHéthelyi and Külshammer showed that the number of conjugacy classes {k(G)} of any solvable finite group G whose order is divisible by the square of a prime p is at least {(49p+1)/60}. Here an asymptotic generalization of this result is established. It is proved that there exists a constant {c>0} such that, for any finite group G whose order is divisible by the square of a prime p, we have {k(G)\geq cp}.

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