• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1063-1073
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• 2014

A finite group G is called a $\mathcal{QNS}$-group if every minimal subgroup X of G is either quasinormal in G or self-normalizing. In this paper the authors classify the non-$\mathcal{QNS}$-groups whose proper subgroups are all $\mathcal{QNS}$-groups.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1165-1178
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• 2009

In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.559-587
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• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.181-190
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• 1998

In this paper we define the concept of anti fuzzy $H_v$-subgroup of an $H_v$ -group and prove a few theorems concerning this concept. We also obtain a necessary and sufficient condition for a fuzzy subset of an $H_v$-group to be an anti fuzzy $H_v$ -subgroup. We also abtain a relation between the fuzzy $H_v$-subgroups and the and the anti fuzzy $H_v$-subgroup.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.201-221
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• 2012

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.1-8
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• 1999

Let $K_{\alpha}(G)$ (resp. $K_s(G)$) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$).

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.627-634
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• 2003

In this paper, we introduce the concepts of t-intuitionistic fuzzy subgroups and t-intuitionistic fuzzy subrings. And we study some properties of t-subgroups and t-subrings.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.457-486
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• 2018

In several fields the soft set theory has a very vast range uses and applications. A soft group is a proper family of subgroups and a fuzzy soft group is a proper family of fuzzy subgroups. Here in this paper the concept of lattice ordered fuzzy soft groups is introduced. Also its some properties are studied and discussed. In addition, the defintion of lattice order fuzzy soft right (left) cosets and lattice order soft product of fuzzy soft subgroups and some related results are discussed to clear these ideas.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.257-266
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• 2023

Let G_k,n(ℍ) for 2 ≤ k < n denote the Grassmann manifold of k-dimensional vector subspaces of ℍⁿ. In this paper, we determine the evaluation subgroups of the Plüker embedding $G{_{2,n}}({\mathbb{H}}){\hookrightarrow}{\mathbb{H}}P^{N-1}$, where $N\;=\;({n \atop 2}\)$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.2
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• pp.154-161
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• 2014

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.