TY - JOUR
T1 - ON p-GROUPS with AUTOMORPHISM GROUPS RELATED to the CHEVALLEY GROUP G2(p)
AU - Bamberg, John
AU - Freedman, Saul D.
AU - Morgan, Luke
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Let be an odd prime. We construct a -group of nilpotency class two, rank seven and exponent , such that induces on the Frattini quotient. The constructed group is the smallest -group with these properties, having order , and when our construction gives two nonisomorphic -groups. To show that satisfies the specified properties, we study the action of on the octonion algebra over , for each power of , and explore the reducibility of the exterior square of each irreducible seven-dimensional -module.
AB - Let be an odd prime. We construct a -group of nilpotency class two, rank seven and exponent , such that induces on the Frattini quotient. The constructed group is the smallest -group with these properties, having order , and when our construction gives two nonisomorphic -groups. To show that satisfies the specified properties, we study the action of on the octonion algebra over , for each power of , and explore the reducibility of the exterior square of each irreducible seven-dimensional -module.
KW - exterior square
KW - G(q)
KW - p-group
UR - http://www.scopus.com/inward/record.url?scp=85078220585&partnerID=8YFLogxK
UR - https://arxiv.org/abs/1710.01497
U2 - 10.1017/S1446788719000466
DO - 10.1017/S1446788719000466
M3 - Article
AN - SCOPUS:85078220585
SN - 1446-7887
VL - 108
SP - 321
EP - 331
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 3
ER -