潘江敏. 任意域上一般线性群周期元素的阶[J]. 云南大学学报(自然科学版), 2005, 27(5): 369-371.
引用本文: 潘江敏. 任意域上一般线性群周期元素的阶[J]. 云南大学学报(自然科学版), 2005, 27(5): 369-371.
PAN Jiang-min. Orders of periodic elements of general linear group over any field[J]. Journal of Yunnan University: Natural Sciences Edition, 2005, 27(5): 369-371.
Citation: PAN Jiang-min. Orders of periodic elements of general linear group over any field[J]. Journal of Yunnan University: Natural Sciences Edition, 2005, 27(5): 369-371.

任意域上一般线性群周期元素的阶

Orders of periodic elements of general linear group over any field

  • 摘要: 设F是任意一个域,GL(m,F)为F上的一般线性群,SF(m)表示GL(m,F)中周期元素的阶数集.对任意正整数n,GL(m,F)中有阶为n的元素的充分必要条件被证明.进一步,若E/F为域扩张,SF(m)=SE(m)的条件被得到.

     

    Abstract: Let F be any field,GL(m,F)be the general linear group over F,SF(m)be the set of orders of periodic elements in GL(m,F).Anecessary and sufficient condition for that there is an element A∈ GL(m,F)such that o(A)=n is proved.Moreover,if E/F is an extension of field,it is addressed a sufficient condition such that SF(m)=SE(m).

     

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