• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.559-569
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• 2004

In this paper we shall discuss the quasi-perfect automata associated with power automata. We shall give the fact that its power automaton is invertible if an automaton A is quasi-perfect. Moreover, some subgroups and normal subgroups of the characteristic semigroup X(M) will have the very interesting parts in their structures.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.737-748
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• 2009

Using the notion of intuitionistic fuzzy subgroups, its roughness is discussed. With respect to a congruence relation on a group, several properties about the lower and upper approximations of a subset of a group are investigated.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1087-1093
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• 2020

The aim of this paper is to show that every Engel quasinormal subgroups of the unit group of a division ring with uncountable center is central.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.781-799
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• 2023

For any bipolar multi Q-fuzzy set δ of an universe set G, we redefined a normal, conjugate concepts, union and product operations of a bipolar M - N-multi Q-fuzzy subgroups and we discuss some of its properties. On the other hand, we introduce and define the level subsets positive β-cut and negative α-cut of bipolar M - N- multi Q- fuzzy subgroup and discuss some of its related properties.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.723-730
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• 2004

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups such as an (${\in},\;{\in}\;{\vee}q$)-fuzzy normal subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy characteristic subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups are obtained.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.365-371
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• 2019

If 𝖃 is a class of groups, denote by F𝖃 the class of groups G such that for every $x{\in}G$, there exists a normal subgroup of finite index H(x) such that ${\langle}x,h{\rangle}{\in}$ 𝖃 for every $h{\in}H(x)$. In this paper, we consider the class F𝖃, when 𝖃 is the class of nilpotent-by-finite, finite-by-nilpotent and periodic-by-nilpotent groups. We will prove that for the above classes 𝖃 we have that a finitely generated hyper-(Abelian-by-finite) group in F𝖃 belongs to 𝖃. As a consequence of these results, we prove that when the nilpotency class of the subgroups (or quotients) of the subgroups ${\langle}x,h{\rangle}$ are bounded by a given positive integer k, then the nilpotency class of the corresponding subgroup (or quotient) of G is bounded by a positive integer c depending only on k.

• The Korean Journal of Physiology
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• v.14 no.1
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• pp.1-5
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• 1980

This study was under taken to investigate the influences of predictable or unpredictable stress upon gastric ulceration, and the hippocampectomy upon the ulceration order the stressful conditions. Sixty male albino rats(Sprague-Dawley strain) were divided equally into 3 groups: One was the hippocampal group(N=20) which received hippocampal ablation by suction, another was the cortical control group(N =20) which received partial cortical ablation over the hippocampus, and a third was the normal control group(N=20). Each group was further divided into two subgroups: One was the predicted subgroup(N=10) in which animals could predict the imminent stressful stimuli by hearing a sound(1,000 Hz, 2 sec in duration) 3 sec before the onset of the stress, and the other was the unpredicted subgroup(N=10). After starvation for 24 hours, but water ad libitum, each rat received the electric stimulation(3 mA, 60 Hz, 2 sec in duration, and once per minute in average) for 6 hours via a pair of electrodes attached on the tale. The electric stimulation served as the stress causing the gastric ulcer. Five hours after completion of stimulation, the stomach filled with the physiological saline was removed under deep anesthesia and spread out on a small glass plate. The numbers of the ulcer in each stomach were counted and the shape was examined under the dissecting microscope. Results obtained were as follows: 1. The mean numbers of the ulcer of the predicted subgroups were significantly larger than those of the unpredicted subgroups in the normal control and the cortical control groups, but there was no difference between the values of the two subgroups in the hippocampal group. 2. The mean numbers of the ulcer of the predicted subgroups in the normal control and the cortical control groups were larger(but not significant) than that in the hippocampal group. It is inferred from the above results that the prediction of the stress strengthens the effect of the stress on the gastric ulceration, and the hippocampus facilitates the effect of the prediction of the stress.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.367-376
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• 2015

In this paper, we classified finite p-groups G such that $$C_G(x)/&lt;x&gt;$$ is cyclic for all non-central elements $x{\in}G$. This solved a problem proposed By Y. Berkovoch.

• Journal of the East Asian Society of Dietary Life
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• v.23 no.1
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• pp.44-52
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• 2013

This study investigated hepatic functional improvement and anti-fibrotic effects of water extracts of black tea. Male Sprague-Dawley rats were divided into four groups (normal, control, and two experimental subgroups: Ba, Bb) and observed for 3 weeks. Liver fibrosis in rats developed from carbon tetrachloride ($CCl_4$) administration, except for the normal group. Except for the normal and control group, the two experimental subgroups were fed water extracts of black tea. The food efficiency ratio significantly increased in the experimental group compared to the control group. The experimental group had a significantly lower liver weight compared to the control group. The ratio of liver weight to body weight was significantly lower in the experimental group than the control group. The levels of aspartate aminotransferase, alanine aminotransferase, alkaline phosphatase, blood urea nitrogen, and low-density lipoprotein-cholesterol in serum significantly decreased in the experimental group compared to the control group. The values of hydroxyproline and malondialdehyde in liver were even lower in the experimental group than the control group. In observations on liver histology, weaker inflammation and fibrosis were observed in the experimental group compared to the control group. In conclusion, water extracts of black tea help hepatic cells keep their functions, restraining and protecting the liver from impairments caused by $CCl_4$ administration, and can be effective as anti-fibrotic agents.