ON ABELIAN SUBGROUPS AND THE CONJUGACY PROBLEM IN FREE PERIODIC GROUPS OF ODD ORDER

1968 ◽  
Vol 2 (5) ◽  
pp. 1131-1144 ◽  
Author(s):  
P S Novikov ◽  
S I Adjan
Keyword(s):  
Conjugacy Problem ◽  
Odd Order ◽  
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.

scholarly journals Centralizers of abelian subgroups in locally finite simple groups

1997 ◽  
Vol 40 (2) ◽  
pp. 217-225
Author(s):  
M. Kuzucuoǧlu
Keyword(s):  
Simple Group ◽  
Finite Length ◽  
Finite Simple Group ◽  
Abelian Subgroup ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Locally Finite ◽  
Odd Order ◽  
Non Linear ◽  
Abelian Subgroups

It is shown that, if a non-linear locally finite simple group is a union of finite simple groups, then the centralizer of every element of odd order has a series of finite length with factors which are either locally solvable or non-abelian simple. Moreover, at least one of the factors is non-linear simple. This is also extended to abelian subgroup of odd orders.

ON FINITE p-GROUPS OF ODD ORDER WITH MANY SUBGROUPS 2-SUBNORMAL

1996 ◽  
Vol 24 (8) ◽  
pp. 2707-2719
Author(s):  
Gemma Parmeggiani ◽  
G. Zacher
Keyword(s):  
Odd Order

A CHARACTERISATION OF CERTAIN FINITE GROUPS OF ODD ORDER

2011 ◽  
Vol 111 (-1) ◽  
pp. 67-76
Author(s):  
Ashish Kumar Das ◽  
Rajat Kanti Nath
Keyword(s):  
Finite Groups ◽  
Odd Order
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