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Lie Representations and Groups of Prime Power Order
Author(s) -
Bryant R. M.,
Kovács L. G.
Publication year - 1978
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-17.3.415
Subject(s) - order (exchange) , library science , citation , mathematics , computer science , mathematics education , finance , economics
Let p be a prime, P a finite non-cyclic p-gvoup and (xd)Q>(P) of the factor group P/$(P), and the map 61-+B is a homomorphism from the automorphism group Aut P of P to the automorphism group of P/$(P). When P/O(P) is regarded as a vector space over the field of order p, the restriction of Aut P to P/(P) is a group of linear transformations of this vector space. Our main result is to establish that every linear group arises in this way.