Groups of order 2048 with three generators and three relations

Groups of order 2048 with three generators and three relations

It is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.

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Veröffentlicht in:International journal of group theory 2012-03, Vol.1 (1), p.29-37
Hauptverfasser: S. Fouladi, R. Orfi
Format: Artikel
Sprache:eng
Schlagworte:
deficiency zero
finite $p$-group
lower exponent-$p$ central series
Schur multiplier
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Zusammenfassung:It is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.
ISSN:2251-7650
2251-7669