Parametrization of all homomorphisms fromPGL(2Z) intoPGL{2,q)
作者:
Q. Mustaq,
期刊:
Communications in Algebra
(Taylor Available online 1992)
卷期:
Volume 20,
issue 4
页码: 1023-1040
ISSN:0092-7872
年代: 1992
DOI:10.1080/00927879208824389
出版商: Gordon and Breach Science Publishers Ltd.
关键词: 20G40;05C25
数据来源: Taylor
摘要:
LetPL(Fq) denote the projective line over a Galois fieldFq. Consider PSL (2, Z ) as a free product of two cyclic groups <x> and <y> of orders 2 and 3. We have shown that any homomorphism fromPSL(2,Z) intoPGL(2,q) can be extended to a homomorphism fromPGL(2Z) intoPGL(2q) except in the case where the order of the image ofxyis 6 but the images ofxandydo not commute inPGL(2q). It has been shown also that every element inPGL(2,q), not of order 1,2 , or 6, is the image ofxyunder some non-degenerate homomorphism. We have parametrized the conjugacy classes of non-degenerate homomorphisms α with the non-trivial elements ofFq. Due to this parametrization we have developed a useful mechanism by which one can construct.
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