docs: update group concept

docs/groups-architecture.md

@@ -117,10 +117,10 @@ CREATE TABLE groups (
   description TEXT,
   inserted_at TIMESTAMP NOT NULL,
   updated_at TIMESTAMP NOT NULL,
-  CONSTRAINT groups_name_unique UNIQUE (name)
+  CONSTRAINT groups_name_unique UNIQUE (LOWER(name))
 );
 
-CREATE INDEX groups_name_index ON groups(name);
+CREATE INDEX groups_name_index ON groups(LOWER(name));
 ```
 
 **Attributes:**
@@ -130,7 +130,7 @@ CREATE INDEX groups_name_index ON groups(name);
 - `inserted_at` / `updated_at` - Timestamps
 
 **Constraints:**
-- `name` must be unique
+- `name` must be unique (case-insensitive, using LOWER(name))
 - `name` cannot be null
 - `name` max length: 100 characters
 - `description` max length: 500 characters
@@ -194,7 +194,7 @@ end
 - `destroy` - Delete group (with confirmation)
 
 **Validations:**
-- `name` required, unique, max 100 chars
+- `name` required, unique (case-insensitive), max 100 chars
 - `description` optional, max 500 chars
 
 #### `Mv.Membership.MemberGroup`
@@ -319,7 +319,7 @@ end
 - Display group badges for each member
 - Badge shows group name
 - Multiple badges if member in multiple groups
-- Click badge to filter by that group
+- *(Optional)* Click badge to filter by that group (enhanced UX, can be added later)
 
 **Filtering:**
 - Dropdown/select to filter by group
@@ -374,7 +374,11 @@ end
 </span>
 ```
 
-**Clickable Group Badge (for filtering):**
+**Clickable Group Badge (for filtering) - Optional:**
+
+**Note:** This is an optional enhancement. The dropdown filter provides the same functionality. The clickable badge improves UX by showing the active filter visually and allowing quick removal.
+
+**Estimated effort:** 1.5-2.5 hours
 
 ```heex
 <button 
@@ -712,13 +716,13 @@ Das MVP umfasst die **grundlegenden Funktionen**, die notwendig sind, um Gruppen
 7. ✅ Nach Gruppen filtern
 8. ✅ Nach Gruppen sortieren
 9. ✅ Gruppen in Mitgliederdetail anzeigen
+10. ✅ Gruppen in Mitgliedersuche (automatisch via search_vector)
 
 **Nicht im MVP:**
 - ❌ Hierarchische Gruppen
 - ❌ Rollen/Positionen in Gruppen
 - ❌ Erweiterte Gruppenattribute (Datum, Status, etc.)
 - ❌ Gruppen-spezifische Berechtigungen
-- ❌ Gruppen in Mitgliedersuche (kann später kommen)
 
 ### Fachliche Einheiten (Vertikale Slices)
 
@@ -846,11 +850,9 @@ Das MVP umfasst die **grundlegenden Funktionen**, die notwendig sind, um Gruppen
 - ✅ Einheit 3: Gruppen-Verwaltungs-UI
 - ✅ Einheit 4: Gruppen in Mitgliederübersicht
 - ✅ Einheit 5: Gruppen in Mitgliederdetail
+- ✅ Einheit 6: Gruppen in Mitgliedersuche (automatisch via search_vector)
 - ✅ Einheit 7: Berechtigungen
 
-**Optional für MVP (kann später kommen):**
-- ⏸️ Einheit 6: Gruppen in Mitgliedersuche (kann in Phase 2 kommen)
-
 **Total MVP Estimation:** 13-15h
 
 ### Implementierungsreihenfolge
@@ -947,11 +949,13 @@ Jede fachliche Einheit kann als **separates Issue** umgesetzt werden:
 3. Group filter dropdown
 4. Group sorting
 5. URL query param persistence
+6. *(Optional)* Clickable group badges for filtering (enhanced UX)
 
 **Deliverables:**
 - Groups visible in member overview
-- Filter by group
+- Filter by group (via dropdown)
 - Sort by group
+- *(Optional)* Clickable badges for quick filtering
 
 **Estimation:** 2-3h
 
@@ -1046,12 +1050,14 @@ Jede fachliche Einheit kann als **separates Issue** umgesetzt werden:
 - Group filter dropdown
 - Group sorting
 - URL persistence
+- *(Optional)* Clickable group badges for filtering
 
 **Acceptance Criteria:**
 - Groups visible in member overview
-- Can filter by group
+- Can filter by group (via dropdown)
 - Can sort by group
 - Filter persists in URL
+- *(Optional)* Can filter by clicking group badge
 
 ### Issue 4: Member Detail - Groups Display
 **Type:** Frontend  
@@ -1069,13 +1075,16 @@ Jede fachliche Einheit kann als **separates Issue** umgesetzt werden:
 **Type:** Backend  
 **Estimation:** 2h  
 **Tasks:**
-- Update search vector trigger
-- Extend fuzzy search
-- Test search
+- Update search vector trigger to include group names
+- Extend fuzzy search to search group names
+- Test search functionality
 
 **Acceptance Criteria:**
-- Group names searchable in member search
+- Group names searchable in member search (automatic via search_vector)
 - Search finds members by group name
+- Search vector updates automatically when member-group associations change
+
+**Note:** This is part of MVP as group names are automatically included in full-text search once the search_vector trigger is updated.
 
 ### Issue 6: Authorization
 **Type:** Backend/Frontend  
@@ -1132,11 +1141,12 @@ defmodule Mv.Membership.GroupTest do
       assert %{name: ["has already been taken"]} = errors_on(changeset)
     end
 
-    test "name uniqueness is case-sensitive" do
+    test "name uniqueness is case-insensitive" do
       Group.create!(%{name: "Vorstand"})
       attrs = %{name: "VORSTAND"}
-      # For MVP: case-sensitive uniqueness
-      assert {:ok, _} = Group.create(attrs)
+      # Name uniqueness should be case-insensitive
+      assert {:error, changeset} = Group.create(attrs)
+      assert %{name: ["has already been taken"]} = errors_on(changeset)
     end
 
     test "allows description to be nil" do
@@ -1458,8 +1468,8 @@ create table(:groups, primary_key: false) do
   add :updated_at, :utc_datetime_usec, null: false
 end
 
-create unique_index(:groups, [:name])
-create index(:groups, [:name])
+create unique_index(:groups, [fragment("LOWER(name)")], name: :groups_name_unique)
+create index(:groups, [fragment("LOWER(name)")], name: :groups_name_index)
 ```
 
 **Migration 2: Create member_groups join table**