• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.393-402
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• 1998

In this paper we describe the results of computations to find symmetric presentations based on minimal conjugate generating pairs for the 32 non-abelian simple groups of order less than one million.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.2C
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• pp.149-154
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• 2008

One of the criteria for designing good LD-STBC is maximizing the mutual information between the transmit and receive signals. In this paper, we propose a construction method of $2^k{\times}2^k$ LD-STBC by selecting the dispersion matrices among the representations of the non-abelian group $G_{m,r}$, of order $2^{k+2}$.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.405-417
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• 2023

The RIP of rings was introduced by Kwak and Lee as a generalization of the one-sided idempotent-reflexivity property. In this study, we focus on rings in which all one-sided semicentral idempotents are central, and we refer to them as quasi-Abelian rings, extending the concept introduced by RIP. We establish that quasi-Abelianity extends to various types of rings, including polynomial rings, power series rings, Laurent series rings, matrices, and certain subrings of triangular matrix rings. Furthermore, we provide comprehensive proofs for several results that hold for RIP and are also satisfied by the quasi-Abelian property. Additionally, we investigate the structural properties of minimal non-Abelian quasi-Abelian rings.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.2
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• pp.764-785
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• 2018

In this paper, we present a new public key encryption scheme with equality test (PKEwET). Compared to other PKEwET schemes, we find that its security can be improved since the proposed scheme is based on non-Abelian factorization problems. To our knowledge, it is the first scheme regarding equality test that can resist quantum algorithm attacks. We show that our scheme is one-way against chosen-ciphertext attacks in the case that the computational Diffie-Hellman problem is hard for a Type-I adversary. It is indistinguishable against chosen-ciphertext attacks in the case that the Decisional Diffie-Hellman problem is hard in the random oracle model for a Type-II adversary. To conclude the paper, we demonstrate that our scheme is more efficient.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.407-419
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• 2009

The simple non-associative algebra $N(e^{A_S},q,n,t)_k$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$ and its antisymmetrized algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$. We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations $Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)$ of te antisymmetrized algebra $WN(e^{{\pm}x^r}0,2)_B^-$ and every derivation of the algebra is outer in this paper.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.21-59
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• 2020

Let L_K denote the hypothetical automorphic Langlands group of a number field K. In our recent study, we briefly introduced a certain unconditional non-commutative topological group ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$, called the Weil-Arthur idèle group of K, which, assuming the existence of L_K, comes equipped with a natural topological group homomorphism $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K that we called the "Langlands form" of the global nonabelian norm-residue symbol of K. In this work, we present a detailed construction of ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ and $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K, and discuss their basic properties.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• 한국초전도학회:학술대회논문집
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• v.16
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• pp.18-18
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• 2006

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.307-330
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• 2013

If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.