The number of subgroups of a finite abelian p-group of rank 4

Chew, C. Y.; Chin, A. Y. M.; Lim, C. S.

doi:10.1063/1.4932475

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…Remark 2. In an unpublished paper [7], Chew, Chin, and Lim derive an explicit formula for the number of subgroups of a finite abelian p-group of rank 4. Here we will use the formula to reprove the above theorem and also prove one more conjecture by Tóth in [25, Conjecture 9].…”

Section: 2mentioning

confidence: 99%

Counting subgroups of fixed order in finite abelian groups

Admasu¹,

Sehgal²

2018

Preprint

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We use recurrence relations to derive explicit formulas for counting the number of subgroups of given order (or index) in rank 3 finite abelian p-groups and use these to derive similar formulas in few cases for rank 4. As a consequence, we answer some questions by M. Tärnäuceanu in [24] and L. Tóth in [25]. We also use other methods such as the method of fundamental group lattices introduced in [24] to derive a similar counting function in a special case of arbitrary rank finite abelian p-groups.

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Section: 2mentioning

confidence: 99%

Counting subgroups of fixed order in finite abelian groups

Admasu¹,

Sehgal²

2018

Preprint

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“…Regardless the mechanism of acute angle closure, studies have shown that ALPI can be used as an initial treatment in some cases. [ 108 , 109 ] While LPI serves as the classic initial intervention to reduce IOP in cases of acute angle closure due to pupillary block, the presence of corneal edema might hinder a clear view to safely perform the procedure. [ 109 ] In such cases, ALPI was found to be a safe alternative in reducing IOP.…”

Section: Introductionmentioning

confidence: 99%

“…[ 108 , 109 ] While LPI serves as the classic initial intervention to reduce IOP in cases of acute angle closure due to pupillary block, the presence of corneal edema might hinder a clear view to safely perform the procedure. [ 109 ] In such cases, ALPI was found to be a safe alternative in reducing IOP. Subsequently, as corneal edema subsides, definitive treatment with LPI can be pursued.…”

Section: Introductionmentioning

confidence: 99%

Contemporary Approach to Narrow Angles

Shamseldin Shalaby,

Reddy,

Razeghinejad

et al. 2024

JOVR

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Glaucoma is the leading cause of irreversible blindness worldwide. Among all glaucoma types,primary angle closure glaucoma (PACG) affects approximately 23 million people worldwide, andis responsible for 50% of glaucoma-related blindness, highlighting the devastating consequencesof this disease. The main mechanism of PACG is relative pupillary block. High-risk populations arefemale gender, Asian ethnicity, high hyperopia, short axial length, and a thick/anteriorly positionedlens. This review discusses the clinical diagnosis, classification, and management of patients witha narrow angle with and without intraocular pressure (IOP) elevation and glaucomatous opticnerve damage, including laser peripheral iridotomy (LPI), endocycloplasty (ECPL), lens extraction,and goniosynechialysis.

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“…The order of the direct product G × H is the product of the orders of G and H. i.e., |G × H| = |G||H| [11] The following are some elementary properties of direct products; Let G and H be any two groups, then: (iii.) If G and H are both cyclic finite groups and their orders have no common divisor greater than 1, i.e.…”

mentioning

confidence: 99%

Direct Product of Finite Abelian Group

G¹

2023

IJASR

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In this project, finite abelian groups with some theoretical and algebraic structures are considered. The order of each group is factorized completely with factor of higher multiplicity where necessary. This unique factorization will allow for a way of building new groups and understanding a given group better. Essentially, it provides a way of relating the given group to the direct products of some of its subgroups. Finally, it also reveals how a group of a finite order is isomorphically related to one of the direct products satisfying certain relatively prime condition.

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The number of subgroups of a finite abelian p-group of rank 4

Cited by 3 publications

References 2 publications

Counting subgroups of fixed order in finite abelian groups

Counting subgroups of fixed order in finite abelian groups

Contemporary Approach to Narrow Angles

Direct Product of Finite Abelian Group

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