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A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

  • LI, JINBAO (Chongqing Key Laboratory of Group & Graph Theories and Applications Chongqing University of Arts and Sciences) ;
  • SHI, WUJIE (Chongqing Key Laboratory of Group & Graph Theories and Applications Chongqing University of Arts and Sciences) ;
  • YU, DAPENG (Chongqing Key Laboratory of Group & Graph Theories and Applications Chongqing University of Arts and Sciences)
  • Received : 2014.10.16
  • Published : 2015.11.30

Abstract

In this paper, we characterize some PGL(2, q) by their orders and maximum element orders. We also prove that PSL(2, p) with $p{\geqslant}3$ a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if $q=p^n$ with p a prime and n > 1, PGL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.

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