A Deficiency Zero Presentation for <i>SL</i>
(2, <i>p</i>
)

Campbell, C. M.; Robertson, E. F.

doi:10.1112/blms/12.1.17

Cited by 35 publications

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“…Since a is primitive in GF{p n ) there is a positive integer k for which 1 + a = a* so f(t) = 1 + t -t k is an appropriate trinomial. Note that [5] On presentations of PSL (2,p n ) 337…”

Section: Let a Be A Primitive Element Ofgf(p") Which Is A Zero Of Thementioning

confidence: 99%

On presentation of PSL (2, pⁿ)

1990

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We give presentations for the groups PSL(2,p"), p prime, which show that the deficiency of these groups is bounded below. In particular, for p = 2 where SL(2,2") = PSL(2,2"), we show that these groups have deficiency greater than or equal to -2 . We give deficiency -1 presentations for direct products of SL(2,2"') for coprime n,-. Certain new efficient presentations are given for certain cases of the groups considered.

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“…Since a is primitive in GF{p n ) there is a positive integer k for which 1 + a = a* so f(t) = 1 + t -t k is an appropriate trinomial. Note that [5] On presentations of PSL (2,p n ) 337…”

Section: Let a Be A Primitive Element Ofgf(p") Which Is A Zero Of Thementioning

confidence: 99%

On presentation of PSL (2, pⁿ)

1990

Self Cite

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“…We also point out the connection between a, b | a 5 = (ab) 2 = b m+3 a −n b m a −n = 1 and P SL (2,5). We give a new efficient presentation for P SL (2,5). The notation used in this paper is reasonably standard.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper,we shall be interested in the group defined by the presentation of the form a, b | a 5 = (ab) 2 = b m+3 a −n b m a −n = 1 where m, n ∈ . We also point out the connection between a, b | a 5 = (ab) 2 = b m+3 a −n b m a −n = 1 and P SL (2,5). We give a new efficient presentation for P SL (2,5).…”

Section: Introductionmentioning

confidence: 99%

“…A group C of maximal order with the properties that there is a subgroup A with A Z(C) ∩ C and C/A ∼ = G is called a covering group of G. In general C is not unique but A is unique and is called the Schur multiplier M (G) of G. For details see [1,6,14]. If G is perfect then it was proved in [2] that G has a unique covering group which we denote by G − .…”

Section: Introductionmentioning

confidence: 99%

“…

A new efficient presentation for P SL (2,5) In this paper, we study the structure of G(3, m, n). We also give a new efficient presentation for the Projective Special Linear group P SL(2, 5) and in particular we prove that P SL(2, 5) is isomorphic to G(3, m, n) under certain conditions.

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confidence: 99%

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