The Modular Isomorphism Problem for small groups – revisiting Eick's algorithm

Margolis, L.; Moede, Tobias

doi:10.1016/j.jaca.2022.100001

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…Query optimization is a sophisticated task, and validating its precision and effectiveness requires using relational algebra. This includes various classification and sorting techniques, such as the modular isomorphism problem, which assesses the performance of similar morphological groups and group classification by performance [22,23]. AI Models like deep learning (DL) models, convolutional neural networks (CNNs), and recurrent neural networks (RNNs) have been barely used in solving information security problems such as attack detection [24].…”

Section: Concerning Mlp-kmeansmentioning

confidence: 99%

A Clustering and PL/SQL-Based Method for Assessing MLP-Kmeans Modeling

Silva-Blancas,

Jiménez-Hernández,

Herrera-Navarro

et al. 2024

Computers

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With new high-performance server technology in data centers and bunkers, optimizing search engines to process time and resource consumption efficiently is necessary. The database query system, upheld by the standard SQL language, has maintained the same functional design since the advent of PL/SQL. This situation is caused by recent research focused on computer resource management, encryption, and security rather than improving data mining based on AI tools, machine learning (ML), and artificial neural networks (ANNs). This work presents a projected methodology integrating a multilayer perceptron (MLP) with Kmeans. This methodology is compared with traditional PL/SQL tools and aims to improve the database response time while outlining future advantages for ML and Kmeans in data processing. We propose a new corollary: hk→H=SSE(C),wherek>0and∃X, executed on application software querying data collections with more than 306 thousand records. This study produced a comparative table between PL/SQL and MLP-Kmeans based on three hypotheses: line query, group query, and total query. The results show that line query increased to 9 ms, group query increased from 88 to 2460 ms, and total query from 13 to 279 ms. Testing one methodology against the other not only shows the incremental fatigue and time consumption that training brings to database query but also that the complexity of the use of a neural network is capable of producing more precision results than the simple use of PL/SQL instructions, and this will be more important in the future for domain-specific problems.

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Section: Concerning Mlp-kmeansmentioning

confidence: 99%

A Clustering and PL/SQL-Based Method for Assessing MLP-Kmeans Modeling

Silva-Blancas,

Jiménez-Hernández,

Herrera-Navarro

et al. 2024

Computers

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“…We will use a group base approximation for this case (Lemmas 4.17 to 4. 19). What will be used to distinguish modular group algebras for the rest of the cases is summarized in Table 1.…”

Section: Non-isomorphic Modular Group Algebrasmentioning

confidence: 99%

“…We note that computer experiments for the remaining cases in Propositions 4.2 and 4.5 show that the group-theoretical invariants contained in a GAP package ModIsomExt [18,19] do not give new information on whether the algebras in question are isomorphic. 4.2.…”

Section: Non-isomorphic Modular Group Algebrasmentioning

confidence: 99%

Non-isomorphic 2-groups with isomorphic modular group algebras

Diego

Margolis

Río

2021

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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The Modular Isomorphism Problem and Abelian Direct Factors

García-Lucas

2023

Mediterr. J. Math.

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Let p be a prime and let G be a finite p-group. We show that the isomorphism type of the maximal abelian direct factor of G, as well as the isomorphism type of the group algebra over $${{\mathbb {F}}}_p$$ F p of the non-abelian remaining direct factor, if existing, are determined by $${{\mathbb {F}}}_p G$$ F p G , generalizing the main result in Margolis et al. (Abelian invariants and a reduction theorem for the modular isomorphism problem, Journal of Algebra 636, 533-559 (2023)) over the prime field. To do this, we address the problem of finding characteristic subgroups of G such that their relative augmentation ideals depend only on the k-algebra structure of kG, where k is any field of characteristic p, and relate it to the modular isomorphism problem, extending and reproving some known results.

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The Modular Isomorphism Problem for small groups – revisiting Eick's algorithm

Cited by 4 publications

References 21 publications

A Clustering and PL/SQL-Based Method for Assessing MLP-Kmeans Modeling

A Clustering and PL/SQL-Based Method for Assessing MLP-Kmeans Modeling

Non-isomorphic 2-groups with isomorphic modular group algebras

The Modular Isomorphism Problem and Abelian Direct Factors

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