definition of finite product of subsets of group
Topics
About: group
The table of contents of this article
Starting Context
- The reader knows a definition of group.
- The reader knows a definition of indexed set.
Target Context
- The reader will have a definition of finite product of subsets of group.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( G\): \(\in \{\text{ the groups }\}\)
\( J\): \(\in \{\text{ the finite index sets }\}\), \(= \{j_1, ..., j_n\}\)
\( \{S_j \subseteq G\}_{j \in J}\): \(\in \{\text{ the indexed sets }\}\)
\(*S_{j_1} ... S_{j_n}\): \(= \{s_{j_1} ... s_{j_n} \in G \vert s_{j_1} \in S_{j_1}, ..., s_{j_n} \in S_{j_n}\}\)
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Conditions:
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2: Note
When an \(S_{j_l}\) is a \(1\)-point subset, \(\{s_{j_l}\}\), a notation replaces \(S_{j_l}\) with \(s_{j_l}\): if an element appears as a factor of a finite product of subsets of group, that means the finite product of subsets of group with the element replaced with the \(1\)-point subset.
