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url url
  2. Weltenzyklopädie
  3. گروه متناهیاً تولیدشده
گروه متناهیاً تولیدشده
از ویکی‌پدیا، دانشنامهٔ آزاد
گروه دووجهی از مرتبه ۸، همانگونه که در شکل فوق نشان داده شده، نیاز به دو مولد دارد.

در جبر، گروه متناهیاً تولیدشده (به انگلیسی: Finitely Generated Group)، گروهی چون G است که مجموعه مولد آن S، متناهی باشد؛ یعنی هر عنصر از G را بتوان به صورت ضرب تعداد متناهی از عناصر مجموعه متناهی S یا معکوس‌هایشان نوشت.[۱]

براساس تعریف هر گروه متناهی، متناهیاً تولید شده است، چرا که S را می‌توان خود G در نظر گرفت. هر گروه متناهیاً تولید شده باید شمارا باشد، اما گروه‌های شمارا لزوماً متناهیاً تولید شده نیستند. گروه جمعی اعداد گویای ، مثالی از گروه‌های شمارایی است که متناهیاً تولید شده نمی‌باشد.

ارجاعات

[ویرایش]
  1. ↑ Gregorac, Robert J. (1967). "A note on finitely generated groups". Proceedings of the American Mathematical Society. 18 (4): 756. doi:10.1090/S0002-9939-1967-0215904-3.

منابع

[ویرایش]
  • Rose, John S. (2012) [unabridged and unaltered republication of a work first published by the Cambridge University Press, Cambridge, England, in 1978]. A Course on Group Theory. Dover Publications. ISBN 978-0-486-68194-8.
آیکون خرد

این یک مقالهٔ خرد جبر است. می‌توانید با گسترش آن به ویکی‌پدیا کمک کنید.

برگرفته از «https://fa.wikipedia.org/w/index.php?title=گروه_متناهیاً_تولیدشده&oldid=39854223»
Pusat Layanan

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