Structure of a group and the structure of its lattice of subgroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1967
|
| Edition: | 2. print. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 96 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Structure of a group and the structure of its lattice of subgroups |c Michio Suzuki |
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1967 | |
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 10 | |
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Record in the Search Index
| _version_ | 1804136091028029440 |
|---|---|
| adam_text | Contents.
Page
Introduction 1
Chapter I. Groups with a special kind of subgroup lattice 3
1. The distributive law in subgroup lattices 3
2. Modular identity in subgroup lattices 5
3. The Jordan Dedekind chain condition and lower semi modu¬
larity 8
4. Finite groups with a modular lattice of subgroups .... 13
5. Structure of infinite M groups 18
6. Structure of C/M groups 24
7. Complemented groups 26
Chapter II. Isomorphisms of subgroup lattices 31
1. Projectivities 31
2. Projectivities of abelian groups 32
3. Projectivities of locally free groups 36
4. Projectivities of finite groups 37
5. Projectivities of modular groups 39
6. Index preserving projectivities 41
7. The images of normal subgroups under projectivities of finite
groups 47
8. The number of finite groups with given lattice of subgroups . 51
9. The group of auto projectivities 52
10. Projectivities of simple groups 53
11. Characteristic chains of subgroup lattices 55
12. Representation of lattices as subgroup lattices 56
13. The situation preserving mappings 57
Chapter III. Homomorphisms of subgroup lattices 57
1. The kernels of a homomorphism of a subgroup lattice . . 57
2. Complete Z. homomorphisms onto cyclic groups 59
3. General properties of complete L homomorphisms .... 62
4. £ homomorphisms induced by group homomorphisms ... 64
5. Incomplete L homomorphisms 68
6. L homomorphisms of finite groups 70
7. The meet homomorphisms 73
8. Structure of finite groups which admit a proper L homo
morphism 79
9. L homomorphisms onto a nilpotent group 82
Chapter IV. Dualisms of subgroup lattices 85
1. Dualisms (of abelian groups) 85
2. Nilpotent groups with duals 87
3. Finite solvable groups with duals 89
Bibliography 92
Index 95
|
| adam_txt |
Contents.
Page
Introduction 1
Chapter I. Groups with a special kind of subgroup lattice 3
1. The distributive law in subgroup lattices 3
2. Modular identity in subgroup lattices 5
3. The Jordan Dedekind chain condition and lower semi modu¬
larity 8
4. Finite groups with a modular lattice of subgroups . 13
5. Structure of infinite M groups 18
6. Structure of C/M groups 24
7. Complemented groups 26
Chapter II. Isomorphisms of subgroup lattices 31
1. Projectivities 31
2. Projectivities of abelian groups 32
3. Projectivities of locally free groups 36
4. Projectivities of finite groups 37
5. Projectivities of modular groups 39
6. Index preserving projectivities 41
7. The images of normal subgroups under projectivities of finite
groups 47
8. The number of finite groups with given lattice of subgroups . 51
9. The group of auto projectivities 52
10. Projectivities of simple groups 53
11. Characteristic chains of subgroup lattices 55
12. Representation of lattices as subgroup lattices 56
13. The situation preserving mappings 57
Chapter III. Homomorphisms of subgroup lattices 57
1. The kernels of a homomorphism of a subgroup lattice . . 57
2. Complete Z. homomorphisms onto cyclic groups 59
3. General properties of complete L homomorphisms . 62
4. £ homomorphisms induced by group homomorphisms . 64
5. Incomplete L homomorphisms 68
6. L homomorphisms of finite groups 70
7. The meet homomorphisms 73
8. Structure of finite groups which admit a proper L homo
morphism 79
9. L homomorphisms onto a nilpotent group 82
Chapter IV. Dualisms of subgroup lattices 85
1. Dualisms (of abelian groups) 85
2. Nilpotent groups with duals 87
3. Finite solvable groups with duals 89
Bibliography 92
Index 95 |
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| author | Suzuki, Michio 1926-1998 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)464581 (DE-599)BVBBV022117208 |
| dewey-full | 512/.86 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.86 |
| dewey-search | 512/.86 |
| dewey-sort | 3512 286 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. print. |
| format | Book |
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| id | DE-604.BV022117208 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:02Z |
| indexdate | 2024-07-09T20:50:53Z |
| institution | BVB |
| language | English |
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| physical | 96 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Suzuki, Michio 1926-1998 Verfasser (DE-588)172391695 aut Structure of a group and the structure of its lattice of subgroups Michio Suzuki 2. print. Berlin [u.a.] Springer 1967 96 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 10 Group theory Lattice theory Gruppendynamik (DE-588)4022392-9 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Untergruppenverband (DE-588)4461760-4 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Untergruppenverband (DE-588)4461760-4 s 1\p DE-604 Gruppendynamik (DE-588)4022392-9 s 2\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 10 (DE-604)BV005871160 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Suzuki, Michio 1926-1998 Structure of a group and the structure of its lattice of subgroups Ergebnisse der Mathematik und ihrer Grenzgebiete Group theory Lattice theory Gruppendynamik (DE-588)4022392-9 gnd Gruppentheorie (DE-588)4072157-7 gnd Untergruppenverband (DE-588)4461760-4 gnd |
| subject_GND | (DE-588)4022392-9 (DE-588)4072157-7 (DE-588)4461760-4 |
| title | Structure of a group and the structure of its lattice of subgroups |
| title_auth | Structure of a group and the structure of its lattice of subgroups |
| title_exact_search | Structure of a group and the structure of its lattice of subgroups |
| title_exact_search_txtP | Structure of a group and the structure of its lattice of subgroups |
| title_full | Structure of a group and the structure of its lattice of subgroups Michio Suzuki |
| title_fullStr | Structure of a group and the structure of its lattice of subgroups Michio Suzuki |
| title_full_unstemmed | Structure of a group and the structure of its lattice of subgroups Michio Suzuki |
| title_short | Structure of a group and the structure of its lattice of subgroups |
| title_sort | structure of a group and the structure of its lattice of subgroups |
| topic | Group theory Lattice theory Gruppendynamik (DE-588)4022392-9 gnd Gruppentheorie (DE-588)4072157-7 gnd Untergruppenverband (DE-588)4461760-4 gnd |
| topic_facet | Group theory Lattice theory Gruppendynamik Gruppentheorie Untergruppenverband |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT suzukimichio structureofagroupandthestructureofitslatticeofsubgroups |