Topic
Simple Groups
Courses
Courses whose questions include this topic tag.
Questions
This topic is tagged for 23 questions
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Fall 2024 • Question 1
Prove that the alternating group \(A_5\) is the only simple group of order 60.
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Summer 2022 • Question 1
Show there is no simple group of order \(2304 = 2^8 \cdot 3^2 = 256 \cdot 9\).
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Summer 2020 • Question 1
Show there is no simple group of order \(448=2^6\cdot 7\).
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Spring 2020 • Question 3
Prove that there are no simple groups of order \(2^7\cdot 3^2\).
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Fall 2019 • Question 7
Show that there is no simple group of order \(552=2^3\cdot 3\cdot 23\).
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Fall 2018 • Question 2
Let \(G\) be a finite simple group with identity \(e\). Suppose that \(A\) and \(B\) are distinct maximal proper subgroups of \(G\). If \(A\) and \(B\) are abelian, prove that \(A\cap B=\{e\}\).
Hint: Prove that \(A\cap B\) is normal in \(G\).
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Summer 2018 • Question 1
Show there is no simple group of order 144.
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Spring 2018 • Question 1
Show that there is no simple group of order 112. You may use the fact that \(A_7\) is simple.
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Spring 2017 • Question 1
Prove that there is no simple group of order 132.
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Fall 2016 • Question 2
Let \(G\) be a nonabelian simple group. Prove that \(\operatorname {Aut}G\) contains a normal subgroup isomorphic to \(G\).
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Spring 2016 • Question 2
Prove that there are no simple groups of order 90.
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Fall 2015 • Question 2
Prove that there is no simple group of order 192.
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Spring 2014 • Question 2
What is the number of elements of order 11 in a simple group of order 660?
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Fall 2009 • Question 5
Show that there are no simple groups of order 520.
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Fall 2006 • Question 10
Prove that there are no simple groups of order 992.
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Spring 2005 • Question 10
Prove that there are no simple groups of order 1365.
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Fall 2004 • Question 6
Prove that there are no simple groups of order 616.
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Fall 2003 • Question 6
If \(G\) is a simple group of order 60, prove that \(G\) is isomorphic to \(A_5\), the alternating group of degree 5.
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Fall 2002 • Question 5
Show that there are no simple groups of order 616.
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Fall 2001 • Question 2
Show that there are no simple groups of order 132.
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Fall 1999 • Question 1
Show that there are no simple groups of order 1365.
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Fall 1998 • Question 4
Show that there are no simple groups of order 245.
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Fall 1996 • Question 3
Show that there are no simple groups of order 520.