On the Schur multiplier of finite đť‘ť-groups of maximal class
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Renu Joshi
Abstract
In this article, we prove that the Schur multiplier of a finite đť‘ť-group of maximal class of order
Funding source: Ministry of Education, India
Award Identifier / Grant number: 0400422
Funding statement: The research of the author Renu Joshi is supported by PMRF, Ministry of Education, Government of India (PMRF ID – 0400422).
Acknowledgements
The authors would like to thank Professor Bettina Eick and Professor Michael Vaughan-Lee for many helpful comments and encouragement.
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Communicated by: Christopher W. Parker
References
[1] R. D. Blyth and R. F. Morse, Computing the nonabelian tensor squares of polycyclic groups, J. Algebra 321 (2009), no. 8, 2139–2148. 10.1016/j.jalgebra.2008.12.029Suche in Google Scholar
[2] R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311–335. 10.1016/0040-9383(87)90004-8Suche in Google Scholar
[3] B. Eick, Schur multiplicators of finite 𝑝-groups with fixed coclass, Israel J. Math. 166 (2008), 157–166. 10.1007/s11856-008-1025-ySuche in Google Scholar
[4] B. Eick, Computing 𝑝-groups with trivial Schur multiplicator, J. Algebra 322 (2009), no. 3, 741–751. 10.1016/j.jalgebra.2009.03.031Suche in Google Scholar
[5] G. Ellis, HAP–a GAP package, Version 1.29, Release date 07.01.2021, 2021. Suche in Google Scholar
[6]
S. Hatui, V. Kakkar and M. K. Yadav,
The Schur multiplier of groups of order
[7] G. Karpilovsky, The Schur Multiplier, London Math. Soc. Monogr. (N. S.) 2, The Clarendon, New York, 1987. Suche in Google Scholar
[8] C. R. Leedham-Green and S. McKay, The Structure of Groups of Prime Power Order, London Math. Soc. Monogr. (N. S.) 27, Oxford University, Oxford, 2002. 10.1093/oso/9780198535485.001.0001Suche in Google Scholar
[9] P. Moravec, On the Schur multipliers of finite 𝑝-groups of given coclass, Israel J. Math. 185 (2011), 189–205. 10.1007/s11856-011-0106-5Suche in Google Scholar
[10] N. R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. (N. S.) 22 (1991), no. 1, 63–79. 10.1007/BF01244898Suche in Google Scholar
[11] J. Schur, Über die Darstellung der endlichen Gruppen durch gebrochen lineare Substitutionen, J. Reine Angew. Math. 127 (1904), 20–50. 10.1515/crll.1904.127.20Suche in Google Scholar
[12] The GAP Group, GAP – Groups, algorithms, and programming, Version 4.11.1, 2021. Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Fusion systems realizing certain Todd modules
- Diagonal embeddings of finite alternating groups
- Vertex-transitive graphs with local action the symmetric group on ordered pairs
- On the Schur multiplier of finite đť‘ť-groups of maximal class
- A classification of skew morphisms of dihedral groups
- On closed subgroups of precompact groups
- Inertia of retracts in Demushkin groups
- On arithmetic properties of solvable Baumslag–Solitar groups
Artikel in diesem Heft
- Frontmatter
- Fusion systems realizing certain Todd modules
- Diagonal embeddings of finite alternating groups
- Vertex-transitive graphs with local action the symmetric group on ordered pairs
- On the Schur multiplier of finite đť‘ť-groups of maximal class
- A classification of skew morphisms of dihedral groups
- On closed subgroups of precompact groups
- Inertia of retracts in Demushkin groups
- On arithmetic properties of solvable Baumslag–Solitar groups
