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SIM, HYO-SEOB,SONG, HYUN-JONG The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.5
In [7], it was shown that Euclidean rings R of imaginary quadratic integers admit unitary number systems. In this paper, as an application of the result, we obtain all self similar tiles arising from the unitary number systems of R.
NUMBER SYSTEMS PERTAINING TO EUCLIDEAN RINGS OF IMAGINARY QUADRATIC INTEGERS
Sim, Hyo-Seob,Song, Hyun-Jong The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.3
For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.
CONJUGACY CLASSES OF SUBGROUPS OF SPLIT METACYCLIC GROUPS OF PRIME POWER ORDER
Sim, Hyo-Seob Korean Mathematical Society 1998 대한수학회보 Vol.35 No.4
In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.
Sim, Hyo-Seob,Song, Hyun-Jong The Youngnam Mathematical Society 2014 East Asian mathematical journal Vol.30 No.3
In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.
NORMAL EDGE-TRANSITIVE CIRCULANT GRAPHS
Sim, Hyo-Seob,Kim, Young-Won Korean Mathematical Society 2001 대한수학회보 Vol.38 No.2
A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.