Mohsen Amiri

Finite groups determined by the number of element centralizers

ABSTRACT For a finite group G, let |Cent(G)| and ω(G) denote the number of centralizers of its elements and the maximum size of a set of pairwise noncommuting elements of it, respectively. A group G is called n-centralizer if |Cent(G)| = n and primitive n-centralizer if . In this paper, among other results, we find |Cent(G)| and ω(G) when is minimal nonabelian and this generalizes some previous results. We give a necessary and sufficient condition for a primitive n-centralizer group G with the minimal nonabelian central factor. Also we show that if , then G is a primitive 14-centralizer group and ω(G) = 10 or 13. Finally we confirm Conjecture 2.4 in [A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq. 7(2) (2000), 139-146].

Characterization of finite groups by a bijection with a divisible property on the element orders

ABSTRACT Let G be a finite solvable group of order n and p be a prime divisor of n. In this article, we prove that if the Sylow p-subgroup of G is neither cyclic nor generalized quaternion, then there exists a bijection f from G onto the abelian group such that for each x∈G, the order of x divides the order of f(x).

Finite groups in which at least 1 3 of the elements are involutions

Let G be a finite group and I(G) be the set of the elements x of G such that x2 = 1. In this paper, we characterize all groups G such that |I(G)|≥ |G| 3 and G is not a 2-group.

Parental training and externalizing behaviors of children with severe hearing loss

Background: Externalizing behavior in deaf children causes many psychological problems for their parents. Aggression and rule breaking behaviors in children with severe hearing loss may cause psychological problems in parents and in managing childrens behavior. Consequently, the present study aimed at investigating the effect of parental behavioral training of mothers on reducing the externalized behaviors (aggression and rule breaking behavior) of their 9- to 10- year old children with severe hearing loss. Methods: This was an experimental study with pretest, posttest, and a control group. The research population included all students with severe hearing loss and their mothers. Thus, 30 mothers whose children had the most severe hearing loss were selected as our main sample among 80 mothers who had completed the Child Behavior Checklist. Then, they were placed into the experimental (n=15) and control groups (n=15) after being matched based on age, educational level, and socioeconomic status. The research tool was Child Behavior Checklist-Persian Version. The parental behavior training was provided for the experimental group in nine 90- minute sessions. Results: The results of the present study indicated the effectiveness of experimental treatment on decreasing the aggressive behaviors of children of mothers in the experimental group compared to mothers of the control group (p=0.001). Moreover, the results revealed a decrease in rule breaking behaviors (p= 0.007) in children of mothers of the experimental group compared to mothers of the control group. Conclusion: Parents’ behavioral training is important in decreasing the aggressive and offensive behaviors in children with severe hearing loss who are at risk of behavioral problems. Furthermore, some research has highlighted the necessity of such trainings for parents of these children. Thus, the present study, emphasizing the importance of childhood problems, found that mothers’ behavioral training could prevent behavioral problems of school-aged children with hearing loss and reduce the recurrence of such problems.

Attachment Styles, Parenting Styles, and Depression

The present study aims to examine the relationship between attachment styles, parenting styles of students’ parents, and students’ depression. One hundred and twenty-two university students were selected through random sampling from a total population of 845 graduate students at Zanjan University and were given the Diana Baumrind Parenting Style and Collins and Reid Attachment Style (RAAS) questionnaires and the Beck Depression Inventory. The results of the study demonstrated a significant, negative relationship between parents’ authoritative parenting style and students’ depression; a similar pattern was also seen between secure and ambivalent parents’ attachment style and students’ depression. On the other hand, there was a positive and significant relationship between parents’ permissive and authoritarian parenting style and students’ depression. There was also a positive and significant relationship between parents’ avoidant attachment and students’ depression.

Characterization of

Let

p

G

-groups by sum of the element orders

be a finite group. Then we denote

Sum of the Products of the Orders of Two Distinct Elements in Finite Groups

\psi(G) = \sum_{x\in G}o(x)

A study of mental health and parenting stress among parents of mental disabled children

where