Michael Giudici
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Registered User
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Feb 7 |
awarded | ● Scholar |
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Jan 13 |
accepted | maximal subgroups of finite simple groups |
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Jan 10 |
comment |
Largest permutation group without 2-cycles or 3-cycles It is known that the only primitive group on $n$ points containing a 2-cycle is $S_n$ and any primitive group containing a 3-cycle contains $A_n$. These are classical regults going back to Jordan. Thus any primitive group other than $A_n$ or $S_n$ has no 2-cycles or 3-cycles. There are very good upper bounds on the order of primitive group. The best is by Maroti which says that for such primitive groups one of the following holds: - G is a Mathieu group $M_n$ for $n=11,12,23,24$ -G is a subgroup of $S_m wr S_k$ with $n=m^k$, $m\geq 5$ and $k\geq 2$ -|G|\leq n^{1+\lfloor log_2(n)\rfloor}$ |
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Dec 4 |
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Groups with an automorphism of order two fixing only two elements @Colin: Khukrho's books references a paper by Hartley and Meixner that proves that the group contains a nilpotent subgroup of class at most 2 and index at most an absolute constant. |
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Dec 4 |
awarded | ● Nice Answer |
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Dec 3 |
comment |
Groups with an automorphism of order two fixing only two elements Hi Steve, I am interested in automorphisms of order 2. |
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Dec 2 |
awarded | ● Yearling |
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Dec 2 |
awarded | ● Yearling |
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Dec 2 |
awarded | ● Student |
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Dec 2 |
asked | Groups with an automorphism of order two fixing only two elements |
