Let G be a finite group and
δ
(
G
)
=
1
|
G
|
∑
H
≤
G
{
|
H
|
|
H
is non-cyclic} . In this paper, we show that some arithmetical conditions of
δ
(
G
)
influence the structure of G. Firstly, we prove ...that if
δ
(
G
)
<
13
3
, then G is solvable. Secondly, we determine the structure of finite groups with
δ
(
G
)
≤
2
. Moreover, we prove that if
δ
(
G
)
<
1
+
4
|
G
|
, then G is supersolvable, and we also determine the structure of finite groups G with
δ
(
G
)
=
1
+
4
|
G
|
. Finally, we show that
δ
(
G
)
<
c
does not imply the supersolvability of G for any constant
c
∈
(
1
,
∞
)
.
Problem Statement & Objective: Character tables of maximal subgroups of finite simple groups provide considerable amount of information about the groups. In the present article, our objective is to ...compute the character table of one maximal subgroup of the orthogonal group \(PS{O}_{8}^{+}(3)\). Approach: The projective special orthogonal group \(PS{O}_{8}^{+}(3)\cong {O}_{8}^{+}(3){.2}_{1}\) is obtained from the special orthogonal group \(S{O}_{8}^{+}(3)\) on factoring by the group of scalar matrices it contains. The group \({O}_{8}^{+}(3){.2}_{1}\) has a maximal subgroup of the form 26.S 8 with index 3838185. The group Q ≅ 26 · S 8 is a non-split group extension of an elementary abelian 2-group of order 64 by the symmetric group S 8. We apply the Fischer-Clifford theory to compute the irreducible characters of the extension 26 · S 8. Results and Conclusion: We produce 64 conjugacy classes of elements as well as 64 irreducible character of the non-split group extension 26 · S 8 corresponding to the three inertia factors H 1 = S 8, H 2 = S 6 × 2 and H 3 = (S 4 × S 4):2.
We present a unified explanation for the B-decay anomalies in RD(*) and RK together with the anomalous muon magnetic moment, consistent with the constraints from the current measurements of leptonic ...decay rates and D0−D¯0, Bs0−B¯s0 mixings, within the framework of a minimal left-right symmetric gauge theory motivated by one of the low-energy subgroups of E6 naturally accommodating leptoquarks.
DISTALITY OF CERTAIN ACTIONS ON -ADIC SPHERES SHAH, RIDDHI; YADAV, ALOK KUMAR
Journal of the Australian Mathematical Society (2001),
10/2020, Letnik:
109, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Consider the action of
$\operatorname{GL}(n,\mathbb{Q}_{p})$
on the
$p$
-adic unit sphere
${\mathcal{S}}_{n}$
arising from the linear action on
$\mathbb{Q}_{p}^{n}\setminus \{0\}$
. We show that for ...the action of a semigroup
$\mathfrak{S}$
of
$\operatorname{GL}(n,\mathbb{Q}_{p})$
on
${\mathcal{S}}_{n}$
, the following are equivalent: (1)
$\mathfrak{S}$
acts distally on
${\mathcal{S}}_{n}$
; (2) the closure of the image of
$\mathfrak{S}$
in
$\operatorname{PGL}(n,\mathbb{Q}_{p})$
is a compact group. On
${\mathcal{S}}_{n}$
, we consider the ‘affine’ maps
$\overline{T}_{a}$
corresponding to
$T$
in
$\operatorname{GL}(n,\mathbb{Q}_{p})$
and a nonzero
$a$
in
$\mathbb{Q}_{p}^{n}$
satisfying
$\Vert T^{-1}(a)\Vert _{p}<1$
. We show that there exists a compact open subgroup
$V$
, which depends on
$T$
, such that
$\overline{T}_{a}$
is distal for every nonzero
$a\in V$
if and only if
$T$
acts distally on
${\mathcal{S}}_{n}$
. The dynamics of ‘affine’ maps on
$p$
-adic unit spheres is quite different from that on the real unit spheres.
Background: Along with the implementation of the one-child policy in China, a special group of bereaved parents called 'shiduer' (失独者), meaning parents bereaved by the loss of their only child, ...emerged. Although previous research has examined the physical and psychological health of this population, individual differences in physical and psychological outcomes are still not well understood.
Objective: This study aimed to identify heterogenous subgroups of Chinese bereaved parents who lost their only child based on the physical and psychological health of this population as well as the predictive factors of each subgroup.
Method: Latent profile analysis was used to explore underlying patterns of physical and psychological indicators including subjective physical health, negative psychological outcomes (i.e. depression, post-traumatic stress disorder and prolonged grief disorder) and positive psychological outcomes (i.e. post-traumatic growth) among a sample of Chinese bereaved parents who lost their only child (N = 536). A three-step approach was used to examine the effects of covariates including quality of spousal relationship and recruitment channels on psychological and physical outcomes.
Results: A three-profile model identified severity-based groupings of a 'resilient' subgroup (n = 153), a 'coping' subgroup (n = 338) and a 'dysfunctional' subgroup (n = 45). Less satisfaction with spousal relationship and recruitment from institutions in the community and online self-help groups (vs. offline support groups) are associated with the membership of the 'coping' or 'dysfunctional' subgroup compared to the 'resilient' subgroup.
Conclusions: There is heterogeneity regarding the physical and psychological health of Chinese parents after losing their only child. The predictive effects of the quality of spousal relationship and the recruitment channels could provide directions for professional intervention.
The present work offers a different perspective for the 5-fold symmetric quasicrystallography by employing affine H2 as a subgroup of affine A4. It is shown that the projection of the Voronoi cell of ...the root lattice A4 can be dissociated as identical five decagons up to a rotation tiled by thick and thin rhombuses. Projection of the Voronoi cell of the weight lattice onto the Coxeter plane tessellates the plane with four different tiles: thick and thin rhombuses with different edge lengths and two types of hexagons. Structure of the local dihedral symmetry H2 fixing a particular point on the Coxeter plane is determined.
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