TY - JOUR
T1 - Asymptotics of the number of involutions in finite classical groups
AU - Fulman, Jason
AU - Guralnick, Robert
AU - Stanton, Dennis
AU - Malle, Gunter
N1 - Publisher Copyright:
© de Gruyter 2017.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.
AB - Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.
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U2 - 10.1515/jgth-2017-0011
DO - 10.1515/jgth-2017-0011
M3 - Article
AN - SCOPUS:85028809040
SN - 1433-5883
VL - 20
SP - 871
EP - 902
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 5
ER -