Periodic groups all of whose maximal abelian subgroups are either normal or have a normal complement

1968 ◽  
Vol 3 (1) ◽  
pp. 25-27
Author(s):  
A. N. Fomin
Keyword(s):  
Normal Complement ◽  
Periodic Groups ◽  
Abelian Subgroups

scholarly journals On infinite groups in which all abelian subgroups are locally cyclic

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.

scholarly journals On non-periodic groups with non-Dedekind norm of Abelian noncyclic subgroups

2021 ◽  
Vol 19 ◽  
pp. 83
Author(s):  
F.N. Liman ◽  
M.G. Drushliak
Keyword(s):  
Periodic Groups ◽  
Abelian Subgroups ◽  
Rank 2

Non-periodic groups without free Abelian subgroups of rank 2 with non-Dedekind norm of Abelian noncyclic subgroups are studied.

Golgi Apparatus and Melanogenesis: Ultrastructural Study of a Human Cellular Blue Nevus (Melanocytoma)

1973 ◽  
Vol 31 ◽  
pp. 380-381
Author(s):  
S.R. Allegra
Keyword(s):  
Endoplasmic Reticulum ◽  
Golgi Apparatus ◽  
Ultrastructural Study ◽  
The Other ◽  
Blue Nevus ◽  
Normal Complement ◽  
Golgi Vesicles ◽  
Golgi System ◽  
The Subject ◽  
Cellular Blue Nevus

The respective roles of the ribo somes, endoplasmic reticulum, Golgi apparatus and perhaps nucleus in the synthesis and maturation of melanosomes is still the subject of some controversy. While the early melanosomes (premelanosomes) have been frequently demonstrated to originate as Golgi vesicles, it is undeniable that these structures can be formed in cells in which Golgi system is not found. This report was prompted by the findings in an essentially amelanotic human cellular blue nevus (melanocytoma) of two distinct lines of melanocytes one of which was devoid of any trace of Golgi apparatus while the other had normal complement of this organelle.

scholarly journals Certain locally nilpotent varieties of groups

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.

Completely simple semigroups: free products, free semigroups and varieties

1981 ◽  
Vol 88 (3-4) ◽  
pp. 293-313 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Matrix Representation ◽  
Maximal Subgroups ◽  
Lattice Of Varieties ◽  
Free Products ◽  
Completely Simple Semigroups ◽  
Countable Rank ◽  
Free Semigroups ◽  
Abelian Subgroups ◽  
And Inversion ◽  
Completely Simple

SynopsisThe class CS of completely simple semigroups forms a variety under the operations of multiplication and inversion (x−1 being the inverse of x in its ℋ-class). We determine a Rees matrix representation of the CS-free product of an arbitrary family of completely simple semigroups and deduce a description of the free completely simple semigroups, whose existence was proved by McAlister in 1968 and whose structure was first given by Clifford in 1979. From this a description of the lattice of varieties of completely simple semigroups is given in terms of certain subgroups of a free group of countable rank. Whilst not providing a “list” of identities on completely simple semigroups it does enable us to deduce, for instance, the description of all varieties of completely simple semigroups with abelian subgroups given by Rasin in 1979. It also enables us to describe the maximal subgroups of the “free” idempotent-generated completely simple semigroups T(α, β) denned by Eberhart et al. in 1973 and to show in general the maximal subgroups of the “V-free” semigroups of this type (which we define) need not be free in any variety of groups.

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