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An infinite family of finite $2$-groups with deficiency zero | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 6، شماره 3، آذر 2017، صفحه 45-49 اصل مقاله (170.83 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21213 | ||
| نویسندگان | ||
| Hossein Abdolzadeh* ؛ Reza Sabzchi | ||
| University of Mohaghegh Ardabili | ||
| چکیده | ||
| We determine a new infinite sequence of finite $2$-groups with deficiency zero. The groups have $2$ generators and $2$ relations, they have coclass $3$ and they are not metacyclic. | ||
| کلیدواژهها | ||
| finite $2$-groups؛ deficiency zero؛ Schur multiplicator | ||
| مراجع | ||
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[1] H. Abdolzadeh and B. Eick, On efficient presentations for infinite sequences of 2-groups with fixed coclass, Algebra Colloq., 20 (2013) 561–572.
[2] M. J. Beetham and C. M. Campbell, A note on the Todd-Coxeter coset enumeration algorithm, P. Edinburgh Math. Soc., 20 (1976) 73–79.
[3] G. Havas, M. F. Newman and E. A. O’Brien, Groups of deficiency zero, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 25 (1994) 53–67. [4] D. L. Johnson, Topics in the theory of group presentations, London Mathematical Society Lecture Note Series, 42, Cambridge University Press, Cambridge, 1980.
[5] M. F. Newman, E.A. O’Brien, Classifying 2-groups by coclass, Trans. Amer. Math. Soc., 351 (1999) 131–169.
[6] R. G. Swan, Representations of polycyclic groups, Proc. Amer. Math. Soc., 18 (1967) 573 – 574.
[7] The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.4 (available from www.gap-system.org), 2005. | ||
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