GENERALIZED HYPERCENTERS IN INFINITE GROUPS

James C. Beidleman; Hermann Heineken; Francesko G. Russo

doi:10.1142/s1793557111000034

GENERALIZED HYPERCENTERS IN INFINITE GROUPS

Asian-European Journal of Mathematics ◽

10.1142/s1793557111000034 ◽

2011 ◽

Vol 04 (01) ◽

pp. 21-30

Author(s):

James C. Beidleman ◽

Hermann Heineken ◽

Francesko G. Russo

Keyword(s):

Infinite Groups ◽

Periodic Groups ◽

Generalized Center

We consider the so-called generalized center, defined by Agrawal, in the slightly wider context of periodic groups and try to find out where additional conditions are needed for refinements. In particular we consider the final terms of the corresponding ascending sequences.

Download Full-text

On infinite groups in which all abelian subgroups are locally cyclic

Monatshefte für Mathematik ◽

10.1007/s00605-021-01594-w ◽

2021 ◽

Author(s):

Costantino Delizia ◽

Chiara Nicotera

Keyword(s):

Finite Groups ◽

Abelian Subgroup ◽

Periodic Case ◽

Infinite Groups ◽

Locally Finite ◽

Locally Finite Groups ◽

Periodic Groups ◽

Abelian Subgroups

AbstractThe structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

Download Full-text

On non-periodic groups whose finitely generated subgroups are either permutable or weakly pronormal

Researches in Mathematics ◽

10.15421/241309 ◽

2013 ◽

Vol 21 ◽

pp. 67

Author(s):

T.V. Velychko

Keyword(s):

Finitely Generated ◽

Infinite Groups ◽

Periodic Groups

We consider some infinite groups whose finitely generated subgroups are either permutable or weakly pronormal.

Download Full-text

Certain locally nilpotent varieties of groups

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700033578 ◽

2003 ◽

Vol 67 (1) ◽

pp. 115-119

Author(s):

Alireza Abdollahi

Keyword(s):

Prime Power ◽

Power Exponent ◽

Variety Of Groups ◽

Periodic Groups ◽

Locally Nilpotent

Let c ≥ 0, d ≥ 2 be integers and be the variety of groups in which every d-generator subgroup is nilpotent of class at most c. N.D. Gupta asked for what values of c and d is it true that is locally nilpotent? We prove that if c ≤ 2d + 2d−1 − 3 then the variety is locally nilpotent and we reduce the question of Gupta about the periodic groups in to the prime power exponent groups in this variety.

Download Full-text

Semigroups with few endomorphisms

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700006996 ◽

1969 ◽

Vol 10 (1-2) ◽

pp. 162-168 ◽

Cited By ~ 5

Author(s):

Vlastimil Dlab ◽

B. H. Neumann

Keyword(s):

Cyclic Group ◽

Finite Groups ◽

Automorphism Groups ◽

Infinite Groups ◽

Infinite Cyclic Group

Large finite groups have large automorphism groups [4]; infinite groups may, like the infinite cyclic group, have finite automorphism groups, but their endomorphism semigroups are infinite (see Baer [1, p. 530] or [2, p. 68]). We show in this paper that the corresponding propositions for semigroups are false.

Download Full-text