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Title:
Predstavitve simetričnih in alternirajočih grup
Authors:
ID
Slemenšek, Dijana
(
Author
)
ID
Pagon, Dušan
(
Mentor
)
More about this mentor...
Files:
MAG_Slemensek_Dijana_2014.pdf
(415,99 KB)
MD5: D75E6248DB52C4D820E0F43B573FBBDA
Language:
Slovenian
Work type:
Master's thesis/paper
Typology:
2.09 - Master's Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
V magistrski nalogi so v prvem delu obravnavane osnovne lastnosti simetričnih in alternirajočih grup. V drugem poglavju je podrobnejši pregled osnovne predstavitve grup Sn dolžine O(n), v nadaljnih dveh poglavjih pa je predstavljena celotna konstrukcija predstavitev grup Sm+n in Smn iz grup Sm ter Sn. Zaradi obsežne dolžine predstavitev simetričnih grup so predstavljeni tudi načini zmanjšanja števila povezav in kratke predstavitve teh grup. Za konec so podrobneje opisane tudi alternirajoče grupe in prikazani nekateri primeri kratkih predstavitev za primere simetričnih grup nizkih redov.
Keywords:
simetrična grupa
,
predstavitev grupe
,
alternirajoča grupa
,
generatorji
,
povezave.
Place of publishing:
Maribor
Publisher:
[D. Slemenšek]
Year of publishing:
2014
PID:
20.500.12556/DKUM-45053
UDC:
512.54(043.2)
COBISS.SI-ID:
20803592
NUK URN:
URN:SI:UM:DK:4Z3FZBZY
Publication date in DKUM:
24.09.2014
Views:
2000
Downloads:
248
Metadata:
Categories:
FNM
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Secondary language
Language:
English
Title:
Presentations of symmetric and alternating groups
Abstract:
In the master's thesis we first provide all necessary basic features of the symmetric and alternating groups. Further on, we take a closer look at a basic presentations for these groups with length O(n). In next couple of chapters we present an entire construction of the presentations for groups Sm+n and Smn starting from groups Sm and Sn. Due to quite long standard presentation of symmetric group we show how to shorten the number of relations and present those groups with a short presentation. As a conclusion we also present the alternating groups in more details and give some concrete examples of short presentations for symmetrical groups of small degrees.
Keywords:
symmetric group
,
presentation of a group
,
alternating group
,
generators
,
relations.
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