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==English== |
==English== |
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{{wikipedia}} |
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{{wikibooks}} |
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===Alternative forms=== |
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* {{l|en|theory of groups}} |
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===Noun=== |
===Noun=== |
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{{ |
{{en-noun|-|+}} |
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{{en-noun|head=[[group]] [[theory]]|-}} |
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# {{ |
# {{&lit|en|group|theory|nodot=1}}; a theory about (particular kinds of) groups. |
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#* '''2007''', Hedley G. Dimock, Rachel R. Kass, ''How to Observe Your Group'', Captus Press, 4th Edition, [https://books.google.com.au/books?id=Ry_HUZ1RVwcC&pg=PA3&dq=%22group+theories%22&hl=en&sa=X&ved=0ahUKEwirz6-5v-_WAhXGWLwKHYe7DqcQ6AEILzAC#v=onepage&q=%22group%20theories%22&f=false page 3], |
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#*: After you have read over the seven '''group theories''' you'll be clearer about what makes the most sense to you for the groups with which you want to use your observation skills. |
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#* '''2012''', Stéphanie Delaune, Steve Kremer, Daniel Pasaila, ''Security Protocols, Constraint Systems, and '''Group Theories''''', Bernhard Gramlich, Dale Miller, Ulrike Sattler (editors), ''Automated Reasoning: 6th International Joint Conference'', Springer, LNAI 7364, [https://books.google.com.au/books?id=hoq6BQAAQBAJ&pg=PA165&dq=%22group+theories%22&hl=en&sa=X&ved=0ahUKEwirz6-5v-_WAhXGWLwKHYe7DqcQ6AEIqwEwFw#v=onepage&q=%22group%20theories%22&f=false page 165], |
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#*: In particular we study the case where cryptographic primitives are modelled using a '''''group theory'''''. '''Group theories''' are a special case of monoidal theories which have been extensively studied by F. Baader and W. Nutt [20,6] who have provided a complete survey of unification in these theories. '''Group theories''' include theories for exclusive or and Abelian groups. |
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# {{lb|en|algebra|uncountable}} The mathematical theory of [[group]]s. |
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#* {{quote-book|en|year=1968|editor=Arthur P. Cracknell|title=Applied '''Group Theory''': Selected Readings in Physics|publisher=w:Pergamon Press|pageurl=https://books.google.com.au/books?id=q5g3BQAAQBAJ&pg=PR9&dq=%22group+theory%22%7C%22group+theories%22&hl=en&sa=X&ved=0ahUKEwiJj8-Iuu_WAhUGvbwKHYQeBlg4ZBDoAQinATAY#v=onepage&q=%22group%20theory%22%7C%22group%20theories%22&f=false|page=ix |
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|passage=T<small>HE</small> feeling seems to be developing among physicists that '''group theory''' can be used as and when required, as many other techniques already are, without its being necessary for everyone to study all the whys and wherefores of the mathematical details involved.}} |
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#* '''1995''', Jean Brocas, ''Chapter 4: The Use of '''Group Theory''' in the Study of Non-Rigid Molecules'', Danail Bonchev, D. H. Rouvray (editors), ''Chemical '''Group Theory''': Techniques and Applications'', Gordon and Breach, [https://books.google.com.au/books?id=f8b7ck4NQ8YC&pg=PA133&dq=%22group+theory%22%7C%22group+theories%22&hl=en&sa=X&ved=0ahUKEwiJj8-Iuu_WAhUGvbwKHYQeBlg4ZBDoAQhHMAY#v=onepage&q=%22group%20theory%22%7C%22group%20theories%22&f=false page 133], |
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#*: Planar cis and/or trans internal rotation tunnelling have been discussed in terms of '''group theory''', leading to theoretical spectra which have been compared to experimental work. |
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====Related terms==== |
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* {{l|en|group theoretical}} |
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====Translations==== |
====Translations==== |
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{{trans-top|mathematical theory of groups}} |
{{trans-top|mathematical theory of groups}} |
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* Chinese: |
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⚫ | |||
*: Mandarin: {{t+|cmn|群論|tr=qúnlùn}} |
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⚫ | |||
* French: {{t|fr|théorie des groupes|f}} |
* French: {{t|fr|théorie des groupes|f}} |
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* German: {{t+|de|Gruppentheorie|f}} |
* German: {{t+|de|Gruppentheorie|f}} |
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* Hindi: {{t|hi| समूह सिद्धांत}} |
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* Hungarian: {{t|hu|csoportelmélet}} |
* Hungarian: {{t+|hu|csoportelmélet}} |
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* Icelandic: {{t|is|grúpufræði|f}} |
* Icelandic: {{t|is|grúpufræði|f}} |
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{{trans-mid}} |
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* Italian: {{t|it|teoria dei grupp|f}} |
* Italian: {{t|it|teoria dei grupp|f}} |
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* Japanese: {{t+|ja|群論|tr=ぐんろん, gunron}} |
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* Kazakh: {{t|kk|топтар теориясы}} |
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* Korean: {{t|ko|군론(群論)}} |
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* Latin: {{t|la|theoria catervarum|f}} |
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* Malay: {{t|ms|teori kumpulan}} |
* Malay: {{t|ms|teori kumpulan}} |
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* Portuguese: {{t|pt|teoria dos grupos|f}} |
* Portuguese: {{t|pt|teoria dos grupos|f}} |
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* Spanish: {{t|es|teoría de grupos|f}} |
* Spanish: {{t|es|teoría de grupos|f}} |
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* Swedish: {{t|sv|gruppteori|c}} |
* Swedish: {{t|sv|gruppteori|c}} |
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* Tamil: {{t|ta|குலக் கோட்பாடு}} |
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* Thai: {{t|th|ทฤษฎีกรุป}} |
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* Vietnamese: {{t|vi|lý thuyết nhóm}} ({{t|vi|[[理說]][[𩁱]]}}) |
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{{trans-bottom}} |
{{trans-bottom}} |
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===See also=== |
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* [[Appendix:Glossary of group theory]] |
* [[Appendix:Glossary of group theory]] |
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===Further reading=== |
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[[zh-min-nan:group theory]] |
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* {{pedia|List of group theory topics}} |
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[[id:group theory]] |
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{{topics|en|Group theory}} |
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[[sv:group theory]] |
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[[ta:group theory]] |
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[[zh:group theory]] |
Revision as of 06:43, 24 July 2024
Englisch
Alternative forms
Nomen
group theory (usually uncountable, plural group theories)
- Used other than figuratively or idiomatically: see group, theory; a theory about (particular kinds of) groups.
- 2007, Hedley G. Dimock, Rachel R. Kass, How to Observe Your Group, Captus Press, 4th Edition, page 3,
- After you have read over the seven group theories you'll be clearer about what makes the most sense to you for the groups with which you want to use your observation skills.
- 2012, Stéphanie Delaune, Steve Kremer, Daniel Pasaila, Security Protocols, Constraint Systems, and Group Theories, Bernhard Gramlich, Dale Miller, Ulrike Sattler (editors), Automated Reasoning: 6th International Joint Conference, Springer, LNAI 7364, page 165,
- In particular we study the case where cryptographic primitives are modelled using a group theory. Group theories are a special case of monoidal theories which have been extensively studied by F. Baader and W. Nutt [20,6] who have provided a complete survey of unification in these theories. Group theories include theories for exclusive or and Abelian groups.
- 2007, Hedley G. Dimock, Rachel R. Kass, How to Observe Your Group, Captus Press, 4th Edition, page 3,
- (algebra, uncountable) The mathematical theory of groups.
- 1968, Arthur P. Cracknell, editor, Applied Group Theory: Selected Readings in Physics, Pergamon Press, page ix:
- THE feeling seems to be developing among physicists that group theory can be used as and when required, as many other techniques already are, without its being necessary for everyone to study all the whys and wherefores of the mathematical details involved.
- 1995, Jean Brocas, Chapter 4: The Use of Group Theory in the Study of Non-Rigid Molecules, Danail Bonchev, D. H. Rouvray (editors), Chemical Group Theory: Techniques and Applications, Gordon and Breach, page 133,
- Planar cis and/or trans internal rotation tunnelling have been discussed in terms of group theory, leading to theoretical spectra which have been compared to experimental work.
Related terms
Translations
mathematical theory of groups
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See also
Further reading
List of group theory topics on Wikipedia.Wikipedia