2019; Physical and Mathematical Sciences, 53(1 (248): 23–27
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ON THE POSSIBILITY OF GROUP-THEORETIC DESCRIPTION OF ANEQUIVALENCE RELATION CONNECTED TO THE PROBLEM OFCOVERING SUBSETS IN FINITE FIELDS WITH COSETS OF LINEARSUBSPACES

Davit Sargsyan*

Received: 2025-01-30 · Published: 2019-04-15

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Original title
ON THE POSSIBILITY OF GROUP-THEORETIC DESCRIPTION OF ANEQUIVALENCE RELATION CONNECTED TO THE PROBLEM OFCOVERING SUBSETS IN FINITE FIELDS WITH COSETS OF LINEARSUBSPACES
Author
Davit Sargsyan
Published
2019-04-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2019.53.1.023

Abstract

LetFnqbe ann-dimensional vector space over a finite fieldFq. LetC(Fnq)denote the set of all cosets of linear subspaces inFnq. CosetsH1,H2,...,Hsare called exclusive ifHi6⊆Hj,1≤i<j≤s. A permutationfofC(Fnq)is called aC-permutation, if for any exclusive cosetsH,H1,H2,...,HssuchthatH⊆H1∪H2∪···∪Hswe have:i)cosetsf(H),f(H1),f(H2),...,f(Hs)are exclusive;ii)cosetsf−1(H),f−1(H1),f−1(H2),...,f−1(Hs)are exclusive;iii)f(H)⊆f(H1)∪f(H2)∪···∪f(Hs);vi)f−1(H)⊆f−1(H1)∪f−1(H2)∪···∪f−1(Hs).In this paper we show that the set of allC-permutations ofC(Fnq)is theGeneral Semiaffine Group of degreenoverFq.
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