Advances in Group Theory
and Applications
an open access journal
ISSN 2499–1287
Volume 1 / 2016
Aracne for AGTA
CONTENTS
Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
V.H. Mikaelian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
On some residual properties of the verbal embeddings of
groups
B.A.F. Wehrfritz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Almost fixed-point-free automorphisms of prime power
order
C. Casolo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Groups in which all subgroups are subnormal-by-finite
A. Ballester-Bolinches – J.C. Beidleman – V. Pérez-Calabuig . . 47
Finite groups whose cyclic subnormal subgroups satisfy
certain permutability conditions
L.A. Kurdachenko – J. Otal – I.Ya. Subbotin . . . . . . . . . . . . . . . . . 55
Some remarks about groups of finite special rank
M.R. Dixon – L.A. Kurdachenko – N.N. Semko . . . . . . . . . . . . . 77
On the structure of groups whose non-abelian subgroups
are serial
D.J.S. Robinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
On groups with extreme centralizers and normalizers
F. de Giovanni – M.L. Newell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Splitting properties of hyper-(rank one) groups
B. Brewster – D. Lewis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Maximal subgroup containment in direct products
S. Stonehewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Generalized quasinormal subgroups of order p2
ADV – Perspectives in Group Theory . . . . . . . . . . . . . . . . . . . . . . . . 151
Advances in Group Theory and Applications
c 2016 AGTA - www.advgrouptheory.com/journal
1 (2016),–pp. 1 2
ISSN: 2499-1287
Editorial
It is a great pleasure and a particular honor for me to present the first
issue of the new journal Advances in Group Theory and Applications.
It is published by the non-profit association AGTA, with the aim
of publishing original and high-quality peer-reviewed papers in the
theory of groups and its applications. The mathematical world today
actively investigates numerous cross-disciplinary research problems
in which the theory of groups plays a conspicuous and essential role.
For that reason the provision of a new specialised journal dedicated
entirely to this subject area seems both timely and desirable.
Both the association and the journal wish to become reference
points for young people intending to do research in group theory,
regardless of their geographic origin. To this end the journal will feature a special section (ADV – Perspectives in Group Theory) devoted
to relevant open problems.
Advances in Group Theory and Applications is published as a printed
volume and as an open-access online journal, freely downloadable
from the website of the association, at the address
www.adgrouptheory.com/journal
I wish to thank all members of the Editorial Board for their encouragement, support and expertise when undertaking this venture.
To Marco Trombetti I extend my very special gratitude for his untiring efforts which ensured the smooth and timely completion of this
first issue.
The first issue of Advances in Group Theory and Applications is
dedicated to Prof. Dr. Hermann Heineken, on the occasion of his
eightieth birthday. His major contribution to group theory over the
years is widely acclaimed and greatly valued. I am personally proud
to have had on several occasions the opportunity of working with
2
Editorial
him and benefitting directly from his broad knowledge and friendly
encouragement. I take this opportunity to thank James C. Beidleman,
who first suggested that the publication of a collection of scientific
contributions dedicated to Hermann would be a fitting and appropriate way of marking his special occasion. This volume and all its
contributors fully endorse these sentiments.
Francesco de Giovanni