28206: Difference between revisions
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Arătați că subgrupurile <math>H_1</math>, <math>H_2</math> și <math>H_3</math> au același număr de elemente. </li> | ''Arătați că subgrupurile <math>H_1</math>, <math>H_2</math> și <math>H_3</math> au același număr de elemente.'' </li> | ||
<li> Dacă <math>G = H_1 \cup H_2 \cup H_3</math>, arătați că grupul <math>G</math> este de tip Klein.</li>'' | <li> ''Dacă'' <math>G = H_1 \cup H_2 \cup H_3</math>, ''arătați că grupul <math>G</math> este de [https://ro.wikipedia.org/wiki/Grupul_lui_Klein tip Klein]''.</li>'' | ||
Revision as of 09:21, 3 January 2025
28206 (Dana Heuberger)
Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(G,\cdot\right)} un grup cu elementul neutru care conține subgrupurile proprii, distincte, finite , și , astfel încât pentru orice permutare Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma \in S_3} și orice Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a \in H_{\sigma\left(1\right)} \setminus \left\{e\right\}} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b \in H_{\sigma\left(2\right)} \setminus \left\{e\right\}} , rezultă că Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ab \in H_{\sigma\left(3\right)}} .
- Arătați că subgrupurile Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_1} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_2} și Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_3} au același număr de elemente.
- Dacă Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G = H_1 \cup H_2 \cup H_3} , arătați că grupul Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G} este de tip Klein.