Real and strongly real classes in PGL n (q) and quasi-simple covers of PSL n (q)

Gill, Nick; Singh, Anupam

doi:10.1515/jgt.2010.055

Cited by 7 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following is [4,Lemma 2.4] in the case G = GL(n, F q ), and the proof is exactly the same in the case G = U(n, F q ). Lemma 3.3.…”

Section: Polynomials Over Finite Fieldsmentioning

confidence: 73%

“…In the rest of this section, we follow the same arguments for G = U(n, F q ) as are given for G = GL(n, F q ) in [4,Section 2]. Since many of the details are essentially the same, we will give outlines of proofs with mostly details which are complementary to those given in [4,Section 2].…”

Section: )mentioning

confidence: 99%

“…More recently, N. Gill and A. Singh [3,4] classified the real conjugacy classes of PGL(n, F q ) and SL(n, F q ). They noted [4, after Theorem 2.8] that when q is even or n is odd, the number of real classes of PGL(n, F q ) is equal to the number of real classes of GL(n, F q ) which are contained in SL(n, F q ).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Number of Real Classes in the Finite Projective Linear and Unitary Groups

Amparo

Vinroot²

2019

Glasgow Math. J.

View full text Add to dashboard Cite

We show that for any n and q, the number of real conjugacy classes in PGL(n, F q ) is equal to the number of real conjugacy classes of GL(n, F q ) which are contained in SL(n, F q ), refining a result of Lehrer, and extending the result of Gill and Singh that this holds when n is odd or q is even. Further, we show that this quantity is equal to the number of real conjugacy classes in PGU(n, F q ), and equal to the number of real conjugacy classes of U(n, F q ) which are contained in SU(n, F q ), refining results of Gow and Macdonald. We also give a generating function for this common quantity.

show abstract

“…The following is [4,Lemma 2.4] in the case G = GL(n, F q ), and the proof is exactly the same in the case G = U(n, F q ). Lemma 3.3.…”

Section: Polynomials Over Finite Fieldsmentioning

confidence: 73%

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

On the Number of Real Classes in the Finite Projective Linear and Unitary Groups

Amparo

Vinroot²

2019

Glasgow Math. J.

View full text Add to dashboard Cite

show abstract

“…Tiep and Zalesski [18] have classified all finite simple and quasi-simple groups with the property that all of their classes are real. Gill and Singh [8,9] have classified all of the real and strongly real classes of the finite special and projective linear groups, as well as all quasi-simple covers of the finite projective special linear groups. Gates, Singh, and the second-named author of this paper [7] classified the strongly real classes of the finite unitary group.…”

Section: Introductionmentioning

confidence: 99%

Real classes of finite special unitary groups

Fry

Vinroot

2016

Journal of Group Theory

View full text Add to dashboard Cite

We classify all real and strongly real classes of the finite special unitary group SU n (q). Unless q ≡ 3(mod 4) and n|4, the classification of real classes is similar to that of the finite special linear group SL n (q). We relate strong reality in SU n (q) to strong reality in the finite special orthogonal groups SO ± n (q), and we classify real and strongly real classes in the last case for the group SO ± n (q), when q is odd and n ≡ 2(mod 4).

show abstract

“…Since these cases naturally center around the study of finite simple groups of Lie type, there is interest in understanding the real and strongly real classes of finite groups of Lie type in general. Gill and the second-named author of this paper have completely classified the real and strongly real classes of the finite special linear groups, the finite projective linear groups, and the quasi-simple covers of the finite projective special linear groups [8,9].…”

Section: Introductionmentioning

confidence: 99%

Strongly real classes in finite unitary groups of odd characteristic

Gates¹,

Singh²,

Vinroot³

2014

Journal of Group Theory

Self Cite

View full text Add to dashboard Cite

We classify all strongly real conjugacy classes of the finite unitary group U(n, F q ) when q is odd. In particular, we show that g ∈ U(n, F q ) is strongly real if and only if g is an element of some embedded orthogonal group O ± (n, F q ). Equivalently, g is strongly real in U(n, F q ) if and only if g is real and every elementary divisor of g of the form (t ± 1) 2m has even multiplicity. We apply this to obtain partial results on strongly real classes in the finite symplectic group Sp(2n, F q ), q odd, and a generating function for the number of strongly real classes in U(n, F q ), q odd, and we also give partial results on strongly real classes in U(n, F q ) when q is even.2010 Mathematics Subject Classification: 20G40, 20E45

show abstract

Real and strongly real classes in PGL n (q) and quasi-simple covers of PSL n (q)

Cited by 7 publications

References 14 publications

On the Number of Real Classes in the Finite Projective Linear and Unitary Groups

On the Number of Real Classes in the Finite Projective Linear and Unitary Groups

Real classes of finite special unitary groups

Strongly real classes in finite unitary groups of odd characteristic

Contact Info

Product

Resources

About