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Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL 2 ( q ) for q ≥ 7

Mark L. Lewis, Yanjun Liu, Hung P. Tong-Viet (2018)

Czechoslovak Mathematical Journal

Let G be a finite group and write cd ( G ) for the degree set of the complex irreducible characters of G . The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a , b ∈ cd ( G ) , the total number of (not necessarily different) primes of the greatest common divisor gcd ( a , b ) is at most 2 . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL 2 ( q ) for q ≥ 7 .

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

Groups where each element is conjugate to its certain power

Pál Hegedűs (2013)

Open Mathematics

This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power g n. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.

Groups whose all subgroups are ascendant or self-normalizing

Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)

Open Mathematics

This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972,...

Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

Abdelhafid Badis, Nadir Trabelsi (2011)

Open Mathematics

Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.

Groups whose proper subgroups are locally finite-by-nilpotent

Amel Dilmi (2007)

Annales mathématiques Blaise Pascal

If 𝒳 is a class of groups, then a group G is said to be minimal non 𝒳 -group if all its proper subgroups are in the class 𝒳 , but G itself is not an 𝒳 -group. The main result of this note is that if c > 0 is an integer and if G is a minimal non ( ℒℱ ) 𝒩 (respectively, ( ℒℱ ) 𝒩 c )-group, then G is a finitely generated perfect group which has no non-trivial finite factor and such that G / F r a t ( G ) is an infinite simple group; where 𝒩 (respectively, 𝒩 c , ℒℱ ) denotes the class of nilpotent (respectively, nilpotent of class at most c , locally...

Groups with all subgroups permutable or of finite rank

Martyn Dixon, Yalcin Karatas (2012)

Open Mathematics

In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.

Groups with complete lattice of nearly normal subgroups.

Maria De Falco, Carmela Musella (2002)

Revista Matemática Complutense

A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given.

Groups with Decomposable Set of Quasinormal Subgroups

de Falco, M., de Giovanni, F. (2001)

Serdica Mathematical Journal

A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.

Groups with every subgroup ascendant-by-finite

Sergio Camp-Mora (2013)

Open Mathematics

A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

Currently displaying 301 – 320 of 389