on the nse of some particular groups

Subject Areas : Statistics

Bahareh Asadian ¹ (Dep. Pure Math., Shahrekord Univ., Shahrekord, Iran)
Neda Ahanjideh ² (Dep. Pure math, sharekord univ. Shahrekord, Iran)

Received: 2019-04-10 Accepted : 2021-03-06 Published : 2021-11-22

Keywords: گروه های پوچ توان, مجموعه $nse$, گروه های ۲-فروبنیوس, گروه های فروبنیوس,

Abstract :

For a finite group $ G $, let $ { \rm n s e } ( G ) $ be the set of the number of the elements of the same order in$ G $. In this paper, we first study the set $ n s e $ of a Frobenius group , the set $ { \rm n s e } $ of a $ 2 $- Frobenius group and the set $ { \rm n s e } $ of a nilpotent group. Then, we show that for the finite non-solvable Frobenius group $ G $ with the certain structure and an arbitrary group $ L $ , if $ {\rm n s e } ( G ) = { \rm n s e } ( L ) $, then $ G ≅ L $. Also, a new criterion is presented to recognize nilpotent groups by their $ {\rm n s e }$.

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