ON p-GROUPS with AUTOMORPHISM GROUPS RELATED to the CHEVALLEY GROUP G2(p)

John Bamberg, Saul D. Freedman, Luke Morgan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)321-331
Number of pages11
JournalJournal of the Australian Mathematical Society
Volume108
Issue number3
DOIs
Publication statusPublished - 1 Jun 2020

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