In this paper, the structure of uncountable groups with finitely many normalizers of large subgroups is studied and the connections between this property and other natural finiteness conditions on ...large subgroups of uncountable groups are investigated. In particular, groups in which every large subgroup is close to be normal with the only obstruction of a finite section and groups with finitely many commutator subgroups of large subgroups are considered. Moreover, groups with a finite covering consisting of groups with normal large subgroups are studied.
A group G is called an FP-group if for each element g of G there exists a subgroup X
g
of G such that the index
is finite and
for all subgroups Y of X
g
, that is, if every element of G induces by ...conjugation a power automorphism on a suitable subgroup of finite index of G. Thus groups with finite conjugacy classes have the FP-property, and the aim of this article is to study the behavior of FP-groups in relation to the known theory of FC-groups.
Communicated by Sudarshan Kumar Sehgal
Permutability in uncountable groups De Falco, M.; Evans, M. J.; de Giovanni, F. ...
Annali di matematica pura ed applicata,
10/2018, Letnik:
197, Številka:
5
Journal Article
Recenzirano
A subgroup
X
of a group
G
is called
permutable
if
X
Y
=
Y
X
for all subgroups
Y
of
G
. It is well known that permutable subgroups play an important role in many problems in group theory, and the ...purpose of this paper is to describe the structure of uncountable groups of regular cardinality
ℵ
in which all large subgroups are permutable.
•Measured and calculated components of adrenal function tests were evaluated.•Most components of adrenal function tests offered little value in diagnosis.•Calculated parts of adrenal function tests ...can help exclude adrenocortical tumors.
There is limited information regarding the value of constitutive components of the ACTH stimulation test (ACTHST) and low-dose dexamethasone suppression test (LDDST) including serum baseline cortisol (BC), difference between post-ACTH stimulation cortisol (PC) and BC (ΔACTHC), cortisol concentration 4h after dexamethasone administration (4HC), difference between 4HC and BC (Δ4C), and the difference between cortisol concentration 8h after dexamethasone administration and 4HC (Δ8C). Therefore, the objective of this study was to determine if these components can predict hyperadrenocorticism, pituitary-dependent hyperadrenocorticism (PDH), or functional adrenocortical tumor (FAT) in dogs. Cortisol concentrations were normalized, as fold change (FC), to the PC reference interval upper limit.
A total of 1267 dogs were included, with hyperadrenocorticism diagnosed in 537 (PDH, n=356; FAT, n=28; undetermined, n=153) and excluded in 730. The area under the receiver operating curves for BC, ΔACTHC, 4HC, Δ4C, and Δ8C to predict hyperadrenocorticism were 0.76 (95% confidence interval (CI), 0.73–0.79), 0.91 (95% CI, 0.89–0.93), 0.83 (95% CI, 0.80–0.87), 0.55 (95% CI, 0.50–0.60), and 0.67 (95% CI, 0.62–0.72), respectively. A diagnostic limit of ≥0.78 FC for ΔACTHC had excellent sensitivity (1.00; 95% CI, 0.74–1.00), but poor specificity (0.67; 95% CI, 0.64–0.71), to predict FAT in dogs with a positive ACTHST. A diagnostic limit of ≥−0.26 FC for Δ4C had excellent sensitivity (1.00; 95% CI, 0.79–1.00), but poor specificity (0.21; 95% CI, 0.18–0.26), to predict FAT in dogs with a positive LDDST. In hyperadrenocorticoid dogs that have positive ACTHST or LDDST results, ΔACTHC or Δ4C, respectively, could be used to exclude FAT.
Weakly power automorphisms of groups De Falco, M.; de Giovanni, F.; Musella, C. ...
Communications in algebra,
01/2018, Letnik:
46, Številka:
1
Journal Article
Recenzirano
An automorphism α of a group G is called a weakly power automorphism if it maps every non-periodic subgroup of G onto itself. The aim of this paper is to investigate the behavior of weakly power ...automorphisms. In particular, among other results, it is proved that all weakly power automorphisms of a soluble non-periodic group G of derived length at most 3 are power automorphisms, i.e. they fix all subgroups of G. This result is best possible, as there exists a soluble non-periodic group of derived length 4 admitting a weakly power automorphism, which is not a power automorphism.
On the upper central series of infinite groups DE FALCO, M.; DE GIOVANNI, F.; MUSELLA, C. ...
Proceedings of the American Mathematical Society,
02/2011, Letnik:
139, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Two relevant theorems by R. Baer and P. Hall show that a group is finite over a term with finite ordinal type of its upper central series if and only if it is finite-by-nilpotent. Extending these ...results, we prove here that if G is any group, the hypercentre factor group G/Z̄(G) is finite if and only if G contains a finite normal subgroup N such that G/N is hypercentral (where the hypercentre Z̄(G) of G is defined as the last term of its upper central series).
A group
G
is said to be an
AFC
-
group
if for each element
x
of
G
at least one of the indices
|
C
G
(
x
)
:
⟨
x
⟩
|
and
|
G
:
C
G
(
x
)
|
is finite. Groups with this property appear as a natural ...generalization of those with finite conjugacy classes, and the aim of this paper is to investigate the structure of
AFC
-groups, and in particular the behaviour of their
FC
-centre.
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