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IMPROVEMENT THEOREMS FOR POLYADIC GROUPS H-DERIVED FROM GROUPS

IMPROVEMENT THEOREMS FOR POLYADIC GROUPS H-DERIVED FROM GROUPS DEMONSTRATIO MATHEMATICAVol. X XN o 3-41987Jacek MichalskiIMPROVEMENT THEOREMSFOR POLYADIC GROUPS H-DERIVED FROM GROUPS1. IntroductionThe papers [15]-[17], [6] have been devoted to the b a s i sof a general theory of derived polyadic groups ( f o r the notion of a derived polyadic group (in various meanings) c f .a l s o e . g . [3], [18], [19], [8] , U l - [ 7 ] , [9] - [13]). In part i c u l a r , in [17] we introduced the notion of a C-modificationof a system with respect to a group. As w i l l be pointed outin t h i s paper, the s o - c a l l e d modification theorems r e l a t e dwith that notion enable us to strengthen some basic r e s u l t sof the polyadic group theory, such as the Hosszu theorem andthe Dornte c r i t e r i o n for an n-group to be derived from a group.2. PreliminariesWe s h a l l use the notions, the terminology and notationof [15]-[17] where one can find the d e f i n i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

IMPROVEMENT THEOREMS FOR POLYADIC GROUPS H-DERIVED FROM GROUPS

Demonstratio Mathematica , Volume 20 (3-4): 18 – Jul 1, 1987

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Publisher
de Gruyter
Copyright
© by Jacek Michalski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1987-3-402
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. X XN o 3-41987Jacek MichalskiIMPROVEMENT THEOREMSFOR POLYADIC GROUPS H-DERIVED FROM GROUPS1. IntroductionThe papers [15]-[17], [6] have been devoted to the b a s i sof a general theory of derived polyadic groups ( f o r the notion of a derived polyadic group (in various meanings) c f .a l s o e . g . [3], [18], [19], [8] , U l - [ 7 ] , [9] - [13]). In part i c u l a r , in [17] we introduced the notion of a C-modificationof a system with respect to a group. As w i l l be pointed outin t h i s paper, the s o - c a l l e d modification theorems r e l a t e dwith that notion enable us to strengthen some basic r e s u l t sof the polyadic group theory, such as the Hosszu theorem andthe Dornte c r i t e r i o n for an n-group to be derived from a group.2. PreliminariesWe s h a l l use the notions, the terminology and notationof [15]-[17] where one can find the d e f i n i

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1987

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