scholarly journals On s-quasinormal and c-normal subgroups of a finite group

2008 ◽  
Vol 24 (4) ◽  
pp. 647-654 ◽  
Author(s):  
Shi Rong Li
Keyword(s):  
Finite Group ◽  
Normal Subgroups ◽  
A Finite Group

On S-Quasinormal and C-Normal Subgroups of Prime Power Order in Finite Groups

2011 ◽  
Vol 18 (04) ◽  
pp. 685-692
Author(s):  
Xuanli He ◽  
Shirong Li ◽  
Xiaochun Liu
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Normal Subgroups ◽  
A Finite Group

Let G be a finite group, p the smallest prime dividing the order of G, and P a Sylow p-subgroup of G with the smallest generator number d. Consider a set [Formula: see text] of maximal subgroups of P such that [Formula: see text]. It is shown that if every member [Formula: see text] of is either S-quasinormally embedded or C-normal in G, then G is p-nilpotent. As its applications, some further results are obtained.

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 On extension of characters from normal subgroups

1984 ◽  
Vol 27 (1) ◽  
pp. 7-9 ◽  
Author(s):  
G. Karpilovsky
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Sufficient Condition ◽  
Normal Subgroups ◽  
Complex Character ◽  
A Finite Group

In what follows, character means irreducible complex character.Let G be a finite group and let % be a character of a normal subgroup N. If χ extends to a character of G then χ is stabilised by G, but the converse is false. The aim of this paper is to prove the following theorem which gives a sufficient condition for χ to be extended to a character of G.

scholarly journals Blocks and Normal Subgroups of Finite Groups

1963 ◽  
Vol 22 ◽  
pp. 15-32 ◽  
Author(s):  
W. F. Reynolds
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Irreducible Character ◽  
Normal Subgroups ◽  
Irreducible Characters ◽  
Section 8 ◽  
A Finite Group

Let H be a normal subgroup of a finite group G, and let ζ be an (absolutely) irreducible character of H. In [7], Clifford studied the irreducible characters X of G whose restrictions to H contain ζ as a constituent. First he reduced this question to the same question in the so-called inertial subgroup S of ζ in G, and secondly he described the situation in S in terms of certain projective characters of S/H. In section 8 of [10], Mackey generalized these results to the situation where all the characters concerned are projective.

scholarly journals Topologies on finite groups

1969 ◽  
Vol 1 (3) ◽  
pp. 315-317 ◽  
Author(s):  
Sidney A. Morris ◽  
H.B. Thompson
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Discrete Topology ◽  
Normal Subgroups ◽  
Finite Set ◽  
A Finite Group

It has been shown by D. Stephen that the number N of open sets in a non-discrete topology on a finite set with n elements is not greater than 3 × 2n-2.We show that for admissable topologies on a finite group N ≦ 2n/r, where r is the least order of its non-trivial normal subgroups. This is clearly a sharper bound.

Nilpotent by Supersolvable M-Groups

1985 ◽  
Vol 37 (5) ◽  
pp. 934-962 ◽  
Author(s):  
Alan E. Parks
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Normal Subgroups ◽  
Restrictive Assumption ◽  
Irreducible Characters ◽  
Even Order ◽  
A Finite Group ◽  
Prime 2

A character of a finite group G is monomial if it is induced from a linear (degree one) character of a subgroup of G. A group G is an M-group if all its complex irreducible characters (the set Irr(G)) are monomial.In [1], Dade gave an example of an M-group with a normal subgroup which is itself not an M-group. In his group G, the supersolvable residual N is an extra special 2-group and G/N is supersolvable of even order. Moreover, the prime 2 is used in such a way that no analogous construction is possible in the case that |N| or |G:N| is odd. This led Isaacs in [8] and Dade in [2] to consider the effect of certain “oddness“ hypotheses in the study of monomial characters.Our main results are in the same spirit. Although our techniques seem to require a restrictive assumption on the supersolvable residual of the groups we consider, our theorems provide more evidence that under fairly general circumstances normal subgroups of M-groups should be M-groups.

scholarly journals Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields

1954 ◽  
Vol 2 (2) ◽  
pp. 66-76 ◽  
Author(s):  
Iain T. Adamson
Keyword(s):  
Finite Group ◽  
Exact Sequence ◽  
Cohomology Group ◽  
Cohomology Theory ◽  
Normal Subgroups ◽  
Cohomology Groups ◽  
Coset Space ◽  
Image Position ◽  
A Finite Group

Let G be a finite group, H an arbitrary subgroup (i.e., not necessarily normal); we decompose G as a union of left cosets modulo H:choosing fixed coset representatives v. In this paper we construct a “coset space complex” and assign cohomology groups; Hr([G: H], A), to it for all coefficient modules A and all dimensions, -∞<r<∞. We show that ifis an exact sequence of coefficient modules such that H1U, A')= 0 for all subgroups U of H, then a cohomology group sequencemay be defined and is exact for -∞<r<∞. We also provide a link between the cohomology groups Hr([G: H], A) and the cohomology groups of G and H; namely, we prove that if Hv(U, A)= 0 for all subgroups U of H and for v = 1, 2, …, n–1, then the sequenceis exact, where the homomorphisms of the sequence are those induced by injection, inflation and restriction respectively.

On ${\mathcal U}_c$-Normal Subgroups of Finite Groups

2007 ◽  
Vol 14 (01) ◽  
pp. 25-36 ◽  
Author(s):  
A. Y. Alsheik Ahmad ◽  
J. J. Jaraden ◽  
Alexander N. Skiba
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Subnormal Subgroup ◽  
Normal Subgroups ◽  
Supersoluble Groups ◽  
A Finite Group

Let G be a finite group. We say that a subgroup H of G is [Formula: see text]-normal in G if G has a subnormal subgroup T such that TH = G and (H ∩ T)HG/HG is contained in the [Formula: see text]-hypercenter [Formula: see text] of G/HG, where [Formula: see text] is the class of the finite supersoluble groups. We study the structure of G under the assumption that some subgroups of G are [Formula: see text]-normal in G.

CONTINUOUS TIME QUANTUM WALKS AND QUOTIENT GRAPHS

2011 ◽  
Vol 09 (03) ◽  
pp. 1005-1017
Author(s):  
R. SUFIANI ◽  
S. NAMI ◽  
M. GOLMOHAMMADI ◽  
M. A. JAFARIZADEH
Keyword(s):  
Finite Group ◽  
Continuous Time ◽  
Group Scheme ◽  
Quantum Walks ◽  
Normal Subgroups ◽  
Arbitrary Vertex ◽  
Group Schemes ◽  
Time Quantum ◽  
A Finite Group ◽  
Finite Group Schemes

Continuous-time quantum walks (CTQW) over finite group schemes is investigated, where it is shown that some properties of a CTQW over a group scheme defined on a finite group G induces a CTQW over group scheme defined on G/H, where H is a normal subgroup of G with prime index. This reduction can be helpful in analyzing CTQW on underlying graphs of group schemes. Even though this claim is proved for normal subgroups with prime index (using the Clifford's theorem from representation theory), it is checked in some examples that for other normal subgroups or even non-normal subgroups, the result is also true! It means that CTQW over the graph on G, starting from any arbitrary vertex, is isomorphic to the CTQW over the quotient graph on G/H if we take the sum of the amplitudes corresponding to the vertices belonging to the same cosets.

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