• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.353-375
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• 2006

In this paper we establish a counting method for the Green classes of the Birget-rhodes expansion of finite groups. As an application of the results, we derive explicit enumeration formulas for the Green classes for finite groups of order pq and a finite cyclic group of order $p^m$, where p and q are arbitrary given distinct prime numbers.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• 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 $$C_G(x)/<x>$$ is cyclic for all non-central elements $x{\in}G$. This solved a problem proposed By Y. Berkovoch.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.479-486
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• 2016

The norm N(G) of a group G is the intersection of the normalizers of all the subgroups of G. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group G is cyclic if and only if Aut(G)/P(G) is cyclic, where P(G) is the power automorphism group of G.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.951-960
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• 2022

In this paper, we determine the finite p-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite p-group in which any two distinct 𝓐₁-subgroups generate an 𝓐₂-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.147-151
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• 2004

The purpose of this paper is to investigate the order of a finite p-group and determine the structure of such group.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.205-210
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• 2001

In this paper we will determine Schur multipliers of some finite p-groups of order p$^4$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1835-1843
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• 2018

In this paper, finite p-groups G satisfying $N_G(H){\leq}H^G$ for every non-normal subgroup H of G are completely classified. This solves a problem proposed by Y. Berkovich.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.303-306
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• 2004

There are 49 non-metacyclic p-groups of order less than 1000 with trivial Schur multiplier. In this paper we give a list of deficiency zero presentations for these groups.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.139-144
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• 1995

Two subgroups U and V of a finite group G are called to be p-conjugate for a prime p if a Sylow p-subgroup of U is conjugate to a Sylow p-subgroup of V. This concept of p-conjugacy also makes sense for some infinite groups with a reasonable Sylow theory.