scholarly journals A sufficient condition on centralizers for a finite group to contain a proper CCT subgroup

1976 ◽  
Vol 42 (2) ◽  
pp. 549-556 ◽  
Author(s):  
J.S Williams
Keyword(s):  
Finite Group ◽  
Sufficient Condition ◽  
A Finite Group

Some results on the classification of expansive automorphisms of compact abelian groups

1996 ◽  
Vol 16 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Fabio Fagnani
Keyword(s):  
Finite Group ◽  
Topological Entropy ◽  
Abelian Groups ◽  
Topological Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Abelian Groups ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

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.

Some Characterizations about the Structure of Finite Groups

2012 ◽  
Vol 19 (03) ◽  
pp. 563-568
Author(s):  
Lili Wang ◽  
Guiyun Chen
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Condition ◽  
A Finite Group

A subgroup H of a finite group G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G. The set of all ℋ-subgroups of a finite group G is denoted by ℋ(G). In this paper, a sufficient condition about p-nilpotency is given and some new results for a finite group G to be p-nilpotent or supersolvable are obtained based on the assumption that some subgroups belong to ℋ(G).

scholarly journals On embeddable finite amalgams of groups

1972 ◽  
Vol 13 (2) ◽  
pp. 135-141 ◽  
Author(s):  
Abdul Majeed
Keyword(s):  
Finite Group ◽  
Free Product ◽  
Reduction Theorem ◽  
Sufficient Condition ◽  
A Finite Group

In this paper, a problem of B. H. Neumann and Hanna Neumann [7] about the finite embeddability of an embeddable finite amalgam is discussed. After proving a “reduction theorem” for a finite amalgam to have a finite embedding, we examine some known embeddable amalgams (cf. [3]) as regards their embeddability in a finite group. Since the existence of the generalised free product and the embeddability of an amalgam are synonymous terms, Theorem 3.1 generalises a result in [4]. A sufficient condition for an amalgam of type S to have a finite embedding is also given.

A sufficient condition for nilpotency of the nilpotent residual of a finite group

2018 ◽  
Vol 21 (2) ◽  
pp. 289-293 ◽  
Author(s):  
Agenor Freitas de Andrade ◽  
Alex Carrazedo Dantas
Keyword(s):  
Finite Group ◽  
Sufficient Condition ◽  
Nilpotent Residual ◽  
A Finite Group

AbstractLetGbe a finite group with the property that if{a,b}are powers of{\delta_{1}^{*}}-commutators such that{(|a|,|b|)=1}, then{|ab|=|a||b|}. We show that{\gamma_{\infty}(G)}is nilpotent.

scholarly journals Skew group rings which are Galois

2000 ◽  
Vol 23 (4) ◽  
pp. 279-283
Author(s):  
George Szeto ◽  
Lianyong Xue
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Galois Extension ◽  
Group Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Inner Automorphism ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Skew Group Ring

LetS*Gbe a skew group ring of a finite groupGover a ringS. It is shown that ifS*Gis anG′-Galois extension of(S*G)G′, whereG′is the inner automorphism group ofS*Ginduced by the elements inG, thenSis aG-Galois extension ofSG. A necessary and sufficient condition is also given for the commutator subring of(S*G)G′inS*Gto be a Galois extension, where(S*G)G′is the subring of the elements fixed under each element inG′.

Finite Groups in Which Class Preserving and Central Automorphisms Coincide

2015 ◽  
Vol 22 (spec01) ◽  
pp. 969-974 ◽  
Author(s):  
S. Mohsen Ghoraishi
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Central Automorphisms

A necessary and sufficient condition for the equality of class preserving and central automorphisms of a finite group is given.

A New Cohomological Criterion for the p-Nilpotence of Groups

1998 ◽  
Vol 41 (1) ◽  
pp. 20-22 ◽  
Author(s):  
Maurizio Brunetti
Keyword(s):  
Finite Group ◽  
Sylow Subgroup ◽  
Sufficient Condition ◽  
A Finite Group

AbstractLet G be a finite group, H a copy of its p-Sylow subgroup, and K(n)*(−) the n-th Morava K-theory at p. In this paper we prove that the existence of an isomorphism between K(n)*(BG) and K(n)*(BH) is a sufficient condition for G to be p-nilpotent.

A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups

1977 ◽  
Vol 29 (4) ◽  
pp. 848-855 ◽  
Author(s):  
Martin R. Pettet
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Abelian Group ◽  
Prime Divisor ◽  
Sylow Subgroup ◽  
Elementary Abelian Group ◽  
Sufficient Condition ◽  
Group Of Automorphisms ◽  
Critical Observation ◽  
A Finite Group

Generalizing a celebrated theorem of Thompson, R. P. Martineau has established [4; 5] that a finite group which admits an elementary abelian group of automorphisms with trivial fixed-point subgroup is necessarily solvable. A critical observation in his approach to this problem is the fact that, corresponding to each prime divisor of its order, such a group contains a unique Sylow subgroup invariant (as a set) under the action. Hence, the theorem we shall derive here represents a modest extension of Martineau's result.

Sign in / Sign up

Export Citation Format

Share Document