• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.665-677
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• 2005

The notion of normal intuitionistic fuzzy R-subgroups in near-rings is introduced, and related properties are investigated. Characterization of an intuitionistic fuzzy R-subgroup is given. Using a collection of right R-subgroups, an intuitionistic fuzzy right R-subgroup is established. Using a chain of right R-subgroups, an intuitionistic fuzzy right R-subgroup is also established.

• 충청수학회지
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• 제12권1호
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• pp.163-168
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• 1999

In this paper we discuss another normalization of fuzzy R-subgroups in near-rings.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.231-244
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• 2013

We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence $R_e$ on a group G, the interval-valued congruence class Re is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation * an S=R is well-defined and also we obtain some results related to additional conditions for S. Also we improve that for any two interval-valued fuzzy congruences R and Q on a semigroup S such that $R{\subset}Q$, there exists a unique semigroup homomorphism g : S/R${\rightarrow}$S/G.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.769-772
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• 2022

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r₀ such that for r ≥ r₀, every group G of order p^rm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r₀ in the case where every group of order p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• Journal of Oral Medicine and Pain
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• 제11권1호
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• pp.67-78
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• 1986

This study was attempted to identify the emotional characteristics of temporomandibular disorder patients. The author applied one of the self-report modes of psychological measurement, Symptom Chechlist-90-Revision. The subjects were 219 TM disorder patients who visited the Department of Oral Diagnosis and Oral Medicine, Seoul National University Hospital during the period from December 1985 to September 1986. All the patients were divided into subgroup according sex, age, duration of symptoms, presence or absence of T-scores of each symptom dimension and global index. The obtained result were as follows : 1. Mean value of T-scores of each symptom dimension and global of the overall patients was within normal range. The two higher mean values of T-scores among 9 symptom dimensions were those of SOM and ANX. 2. Mean values of T-scores of females were higher than those of males in the O-C, DEP, ANX, HOS, PSY dimensions and all global indices, and there was a significant difference in the distribution of T-scores of the SOM dimension between males and female(P<0.05). 3. There was no significant difference between the subgroup under 30 years and the subgroup 30 years or older. 4. The subgroup with symptoms for 6 months or longer showed the higher mean values of T-scorers in the SOM, O-C, I-S, DEP, ANX, PHOB, PAR, PSY dimensions and all global indices compared with the subgroup with symptoms for shorter than 6 months. 5. The subgroup with pain showed the higher mean values of T-scores in all the symptom dimensions except the PAR in comparison with the subgroup with other complaints than pain, and there was a significant difference in the distribution of T-scores of the PST index between the pain subgroup and the non-pain subgroup(P<0.05). There was a significant difference in the distribution of T-scores of the PHOB dimension between the high-school graduates subgroup and the college graduates subgroup(P<0.05).

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.653-662
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• 2005

In this paper we shall give the relationships among $T_R,\;End_{R}(M),\;SEnd_{R}(M)\;and\;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M {\times}N){\cong}SAut_{R}(M){\times}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.771-778
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• 2005

In this paper we shall give some group properties derived from the characteristic ring-module $_X(M)$, using the fact that $_X(M)_H$ is a conjugate to $_X(M)_{Ha}$ when M is an invertible right R-module. Also we shall prove that_X(M)$ is group-isomorphic to TR and some normal subgroup properties if M is invertible and R is commutative.

• 대한수학회지
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• 제32권2호
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• pp.289-300
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• 1995

Every group G has a unique maximal normal locally nilpotent subgroup $\Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 \leq R_1 \leq \ldots$ in which $R_{\alpha+1}/R_\alpha = \{Phi(G/R_\alpha)$ for each ordinal $\alpha and R_\beta = \cup_{\alpha<\beta}R_\alpha$ for each limit ordinal $\beta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.

• 대한수학회보
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• 제59권3호
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• pp.781-787
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• 2022

In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra 𝔽_qG can be deduced from a subalgebra 𝔽_q(G/H) of factor group G/H of G, where H is a normal subgroup of G of prime order P. Here, we assume that q = p^r for some prime p and the center of each Wedderburn component of 𝔽_qG is the coefficient field 𝔽_q.