25:
329:
263:
243:
223:
203:
183:
163:
42:
89:
61:
108:
68:
75:
46:
57:
372:
35:
82:
294:
134:
330:"On the influence of transitively normal subgroups on the structure of some infinite groups"
302:
357:
287:
142:
308:
A transitively normal subgroup of a transitively normal subgroup is transitively normal.
298:
248:
228:
208:
188:
168:
148:
366:
271:
126:
122:
24:
130:
145:
of the subgroup is also normal in the whole group. In symbols,
18:
268:
An alternate way to characterize these subgroups is: every
282:
Here are some facts about transitively normal subgroups:
251:
231:
211:
191:
171:
151:
49:. Unsourced material may be challenged and removed.
257:
237:
217:
197:
177:
157:
8:
290:of a transitively normal subgroup is normal.
311:A transitively normal subgroup is normal.
250:
230:
210:
190:
170:
150:
109:Learn how and when to remove this message
321:
277:normal subgroup preserving automorphism
275:of the whole group must restrict to a
165:is a transitively normal subgroup of
16:Property of a subgroup in mathematics
7:
301:is transitively normal. Thus, every
47:adding citations to reliable sources
14:
23:
34:needs additional citations for
58:"Transitively normal subgroup"
1:
297:, or more generally, every
270:normal subgroup preserving
389:
305:is transitively normal.
259:
239:
219:
199:
179:
159:
141:in the group if every
260:
240:
220:
200:
180:
160:
249:
229:
209:
189:
169:
149:
43:improve this article
373:Subgroup properties
139:transitively normal
255:
235:
215:
195:
175:
155:
125:, in the field of
279:of the subgroup.
258:{\displaystyle G}
238:{\displaystyle K}
218:{\displaystyle H}
198:{\displaystyle K}
178:{\displaystyle G}
158:{\displaystyle H}
119:
118:
111:
93:
380:
345:
344:
342:
340:
326:
303:central subgroup
264:
262:
261:
256:
244:
242:
241:
236:
224:
222:
221:
216:
204:
202:
201:
196:
184:
182:
181:
176:
164:
162:
161:
156:
114:
107:
103:
100:
94:
92:
51:
27:
19:
388:
387:
383:
382:
381:
379:
378:
377:
363:
362:
358:Normal subgroup
354:
349:
348:
338:
336:
328:
327:
323:
318:
288:normal subgroup
247:
246:
227:
226:
225:, we have that
207:
206:
187:
186:
167:
166:
147:
146:
143:normal subgroup
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
386:
384:
376:
375:
365:
364:
361:
360:
353:
350:
347:
346:
334:Project Euclid
320:
319:
317:
314:
313:
312:
309:
306:
299:central factor
291:
254:
234:
214:
194:
174:
154:
137:is said to be
117:
116:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
385:
374:
371:
370:
368:
359:
356:
355:
351:
335:
331:
325:
322:
315:
310:
307:
304:
300:
296:
295:direct factor
292:
289:
285:
284:
283:
280:
278:
274:
273:
266:
252:
245:is normal in
232:
212:
192:
185:if for every
172:
152:
144:
140:
136:
132:
128:
124:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
337:. Retrieved
333:
324:
281:
276:
272:automorphism
269:
267:
138:
127:group theory
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
123:mathematics
316:References
205:normal in
69:newspapers
99:June 2022
367:Category
352:See also
131:subgroup
339:30 June
83:scholar
293:Every
286:Every
85:
78:
71:
64:
56:
135:group
133:of a
90:JSTOR
76:books
341:2022
129:, a
62:news
121:In
45:by
369::
332:.
265:.
343:.
253:G
233:K
213:H
193:K
173:G
153:H
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
