The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

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Non-discrete Euclidean buildings for the Ree and Suzuki groups

American Journal of Mathematics ◽

10.1353/ajm.0.0133 ◽

2010 ◽

Vol 132 (4) ◽

pp. 1113-1152 ◽

Cited By ~ 4

Author(s):

Petra Hitzelberger ◽

Linus Kramer ◽

Richard M. Weiss

Keyword(s):

Suzuki Groups ◽

Euclidean Buildings

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Minimal logarithmic signatures for one type of classical groups

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s00200-016-0302-y ◽

2016 ◽

Vol 28 (2) ◽

pp. 177-192

Author(s):

Haibo Hong ◽

Licheng Wang ◽

Haseeb Ahmad ◽

Jun Shao ◽

Yixian Yang

Keyword(s):

Classical Groups ◽

Logarithmic Signatures

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Cryptanalysis of the system based on word problems using logarithmic signatures

Radiotekhnika ◽

10.30837/rt.2021.3.206.09 ◽

2021 ◽

pp. 106-114

Author(s):

Y. Kotukh ◽

T. Okhrimenko ◽

O. Dyachenko ◽

N. Rotaneva ◽

L. Kozina ◽

...

Keyword(s):

Quantum Algorithms ◽

Rapid Development ◽

Difficult Problem ◽

Quantum Computers ◽

Quantum Calculations ◽

Logarithmic Signatures ◽

Public Key Cryptosystems ◽

Asymmetric Cryptography ◽

Complex Problems ◽

Factorization Of Integers

Rapid development and advances of quantum computers are contributing to the development of public key cryptosystems based on mathematically complex or difficult problems, as the threat of using quantum algorithms to hack modern traditional cryptosystems is becoming much more real every day. It should be noted that the classical mathematically complex problems of factorization of integers and discrete logarithms are no longer considered complex for quantum calculations. Dozens of cryptosystems were considered and proposed on various complex problems of group theory in the 2000s. One of such complex problems is the problem of the word. One of the first implementations of the cryptosystem based on the word problem was proposed by Magliveras using logarithmic signatures for finite permutation groups and further proposed by Lempken et al. for asymmetric cryptography with random covers. The innovation of this idea is to extend the difficult problem of the word to a large number of groups. The article summarizes the known results of cryptanalysis of the basic structures of the cryptosystem and defines recommendations for ways to improve the cryptographic properties of structures and the use of non-commutative groups as basic structures.

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Finite simple 3′-groups are cyclic or Suzuki groups

Archiv der Mathematik ◽

10.1007/s00013-014-0630-8 ◽

2014 ◽

Vol 102 (4) ◽

pp. 301-312 ◽

Cited By ~ 4

Author(s):

Imke Toborg ◽

Rebecca Waldecker

Keyword(s):

Suzuki Groups

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BLOCK-TRANSITIVE 5 – (v, k, 2) DESIGNS AND SUZUKI GROUPS

JP Journal of Algebra Number Theory and Applications ◽

10.17654/nt038030271 ◽

2016 ◽

Vol 38 (3) ◽

pp. 271-278

Author(s):

Shaojun Dai ◽

Jing Chen

Keyword(s):

Suzuki Groups

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Attention and Perseverance Behaviors of Preschool Children Enrolled in Suzuki Violin Lessons and Other Activities

Journal of Research in Music Education ◽

10.2307/3345684 ◽

1992 ◽

Vol 40 (3) ◽

pp. 225-235 ◽

Cited By ~ 17

Author(s):

Laurie Scott

Keyword(s):

Preschool Children ◽

The Other ◽

Student Behaviors ◽

Attention Task ◽

Creative Movement ◽

Attending Behavior ◽

Task Variables ◽

Suzuki Groups

The purpose of this study was to examine certain effects of designated activities on attention and persevering behaviors of preschool children. Relationships between teacher reinforcement and student attending behavior were also examined. The subjects, eighty 3- to 5-year-old children, were (a) enrolled in individual Suzuki violin lessons, (b) enrolled in individual and group Suzuki violin lessons, (c) enrolled in creative movement classes, (d) enrolled in preschool activities or classes, or (e) not enrolled in any organized preschool activities or classes. Analysis of classroom and lesson videotapes provided information on teacher and student behaviors. Attention and perseverance behaviors were analyzed through observation of videotape recordings of subjects performing two tasks designed by the experimenter. Both Suzuki groups scored higher on all attention task variables than did children in the other groups. Subjects receiving both individual and group Suzuki violin instruction spent significantly more time on the perseverance task than did all other subjects in the creative movement or preschool group. Teachers of subjects receiving both individual and group Suzuki violin instruction demonstrated significantly more teacher approval than did the preschool or creative movement teachers.

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