• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.25-40
• /
• 2018

We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1395-1399
• /
• 2016

We will classify the finite barely non-abelian p-groups.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1097-1105
• /
• 2015

The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.25 no.3
• /
• pp.567-571
• /
• 2015

Brezing and Weng proposed a method to generate CM parameters of pairing-friendly elliptic curves using polynomial representations of a number field, and Freeman generalized the method for the case of abelian varieties. In this paper we derive explicit formulae to find a family of polynomials used in Brezing-Weng method especially in the case of abelian surfaces, and present some examples generated by the proposed method.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1219-1224
• /
• 2011

In this paper we give a determinant formula for congruent zeta functions of real Abelian function fields. We also give some example of congruent zeta functions when the conductor of real Abelian function field is monic irreducible.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.237-248
• /
• 2009

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered $hyperk{\ddot{a}}hler$ manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.79-83
• /
• 2011

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

• Kyungpook Mathematical Journal
• /
• v.63 no.4
• /
• pp.709-718
• /
• 2023

The inner automorphism groups of quandles are related to the classification problem of quandles. The inner automorphism group of a quandle is generated by inner automorphisms which are presented by columns in the operation table of the quandle. In this paper, we describe inner automorphisms of an abelian extension of a quandle by expressing columns of the operation table of the extended quandle as columns of the operation table of the original quandle. Such a description will be helpful in studying inner automorphism groups of abelian extensions of quandles.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1109-1120
• /
• 2017

For an odd prime p, finite p-groups whose non-abelian subgroups have the same center are classified in this paper.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1689-1696
• /
• 2014

Recently, it was proved that every p-Schur ring over an abelian group of order $p^3$ is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order $p^3$ is Schurian.