Groups of prime-power order having an abelian centralizer of type (r, 1)

1985 ◽  
Vol 99 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Norman Blackburn
Keyword(s):  
Prime Power ◽  
Prime Power Order ◽  
Abelian Centralizer

scholarly journals The energy of integral circulant graphs with prime power order

2011 ◽  
Vol 5 (1) ◽  
pp. 22-36 ◽  
Author(s):  
J.W. Sander ◽  
T. Sander
Keyword(s):  
Adjacency Matrix ◽  
Prime Power ◽  
Prime Power Order ◽  
Circulant Graph ◽  
Closed Formula ◽  
Circulant Graphs ◽  
Vertex Set

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

Space groups and groups of prime-power order II

1980 ◽  
Vol 35 (1) ◽  
pp. 203-209 ◽  
Author(s):  
H. Finken ◽  
J. Neub�ser ◽  
W. Plesken
Keyword(s):  
Prime Power ◽  
Prime Power Order ◽  
Space Groups

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.

scholarly journals Automorphism orbits of finite groups

1986 ◽  
Vol 40 (2) ◽  
pp. 253-260 ◽  
Author(s):  
Thomas J. Laffey ◽  
Desmond MacHale
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Finite Groups ◽  
Prime Power ◽  
Structure Theorem ◽  
Equivalence Classes ◽  
Prime Power Order ◽  
A Finite Group

AbstractLet G be a finite group and let Aut(G) be its automorphism group. Then G is called a k-orbit group if G has k orbits (equivalence classes) under the action of Aut(G). (For g, hG, we have g ~ h if ga = h for some Aut(G).) It is shown that if G is a k-orbit group, then kGp + 1, where p is the least prime dividing the order of G. The 3-orbit groups which are not of prime-power order are classified. It is shown that A5 is the only insoluble 4-orbit group, and a structure theorem is proved about soluble 4-orbit groups.

scholarly journals On c-normality of finite groups

2005 ◽  
Vol 78 (3) ◽  
pp. 297-304 ◽  
Author(s):  
M. Asaad ◽  
M. Ezzat Mohamed
Keyword(s):  
Normal Subgroup ◽  
Finite Groups ◽  
Prime Power ◽  
Prime Power Order

AbstractA subgroup H of a finite G is said to be c-normal in G if there exists a normal subgroup N of G such that G = HN with H ∩ N ≤ HG = CoreG(H). We are interested in studying the influence of the c–normality of certain subgroups of prime power order on the structure of finite groups.

The Laitinen Conjecture for finite non-solvable groups

2012 ◽  
Vol 56 (1) ◽  
pp. 303-336 ◽  
Author(s):  
Krzysztof Pawałowski ◽  
Toshio Sumi
Keyword(s):  
Finite Group ◽  
Fixed Points ◽  
Solvable Group ◽  
Prime Power ◽  
Solvable Groups ◽  
Conjugacy Classes ◽  
Prime Power Order ◽  
Algebraic Condition ◽  
Smooth Action

AbstractFor any finite group G, we impose an algebraic condition, the Gnil-coset condition, and prove that any finite Oliver group G satisfying the Gnil-coset condition has a smooth action on some sphere with isolated fixed points at which the tangent G-modules are not isomorphic to each other. Moreover, we prove that, for any finite non-solvable group G not isomorphic to Aut(A6) or PΣL(2, 27), the Gnil-coset condition holds if and only if rG ≥ 2, where rG is the number of real conjugacy classes of elements of G not of prime power order. As a conclusion, the Laitinen Conjecture holds for any finite non-solvable group not isomorphic to Aut(A6).

A Universal Coefficient Decomposition for Subgroups Induced by Submodules of Group Algebras

1997 ◽  
Vol 40 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Manfred Hartl
Keyword(s):  
Group Algebra ◽  
Prime Power ◽  
Decomposition Theorem ◽  
Group Algebras ◽  
Group Rings ◽  
Prime Power Order ◽  
Relative Dimension ◽  
Theoretical Methods ◽  
Cyclic Groups ◽  
Coefficient Ring

AbstractDimension subgroups and Lie dimension subgroups are known to satisfy a ‘universal coefficient decomposition’, i.e. their value with respect to an arbitrary coefficient ring can be described in terms of their values with respect to the ‘universal’ coefficient rings given by the cyclic groups of infinite and prime power order. Here this fact is generalized to much more general types of induced subgroups, notably covering Fox subgroups and relative dimension subgroups with respect to group algebra filtrations induced by arbitrary N-series, as well as certain common generalisations of these which occur in the study of the former. This result relies on an extension of the principal universal coefficient decomposition theorem on polynomial ideals (due to Passi, Parmenter and Seghal), to all additive subgroups of group rings. This is possible by using homological instead of ring theoretical methods.

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