Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:chap2:2.3_groups

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book:chap2:2.3_groups [2023/10/22 12:48] jvbook:chap2:2.3_groups [2023/10/22 12:53] (current) jv
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   * **a) **  The set is //closed//:  $\quad \forall g_1, g_2 \in G : g_1 \circ g_2 \in G$.   * **a) **  The set is //closed//:  $\quad \forall g_1, g_2 \in G : g_1 \circ g_2 \in G$.
   * **b) **  The set has a //neutral element//:  $\quad \exists e \in G \; \forall g \in G: e \circ g = g$.   * **b) **  The set has a //neutral element//:  $\quad \exists e \in G \; \forall g \in G: e \circ g = g$.
-  * **c) **  Each element has an //inverse element//:   $\quad \forall g \in G \; \exists i \in G : \circ = e$.+  * **c) **  Each element has an //inverse element//:   $\quad \forall g \in G \; \exists i \in G : \circ = e$.
   * **d) **  The operation $\circ$ is //associative//:   $\quad \forall g_1, g_2, g_3 \in G : ( g_1 \circ g_2 ) \circ g_3 = g_1 \circ ( g_2 \circ g_3 )$.   * **d) **  The operation $\circ$ is //associative//:   $\quad \forall g_1, g_2, g_3 \in G : ( g_1 \circ g_2 ) \circ g_3 = g_1 \circ ( g_2 \circ g_3 )$.
 </WRAP> </WRAP>
book/chap2/2.3_groups.1697971735.txt.gz · Last modified: 2023/10/22 12:48 by jv