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visits | member for | 2 years, 7 months |
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I am interesting in Group Theory. I am a fan of John G. Thompson. I have collected many Thompson's published papsers. I alos hope to collect his unpublished notes, letters etc.
Sep 24 |
awarded | Autobiographer |
Jul 2 |
awarded | Curious |
May 23 |
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Does a finite simple group of order divisible by $60$ have $A_{5}$ as a subgroup?
@DerekHolt Yes, it is not sufficient. I forget the condition 60 divives the order of the groups. |
May 23 |
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Does a finite simple group of order divisible by $60$ have $A_{5}$ as a subgroup?
I found this paper: Michael J. J. Barry and Michael B. Ward, SIMPLE GROUPS CONTAIN MINIMAL SIMPLE GROUPS, Publicacions Matem`atiques, Vol 41 (1997), 411–415. By the answer of professor Derek Holt, only Suzuki group left. |
May 23 |
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Does a finite simple group of order divisible by $60$ have $A_{5}$ as a subgroup?
I remember a paper proved that each non abelian simple group contains a minimal simple group as a subgroup. So we need to check minimal simple groups. |
May 29 |
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about the non-solvable group of order $120$
Thank you very much for the inspiring answer. |
May 13 |
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about the non-solvable group of order $120$
Thank you very much, Prof. Holt. |
May 13 |
accepted | about the non-solvable group of order $120$ |
May 13 |
asked | about the non-solvable group of order $120$ |
Mar 25 |
awarded | Critic |
Mar 11 |
awarded | Yearling |
Feb 24 |
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Quotients of Abelian Groups
The only case that need to be considered is that $C=1$. And now the equation is $D/(A+B) \cong A \cap B$. In general, this is not true. So there need some additional restrictions. |
Jan 12 |
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The number of elements of order k in PGL(2, q)
@Mart: Sorry I have no reference on PGL at hand. But I think $1/2$ come from $|G:N_G(C)|$. |
Jan 12 |
answered | The number of elements of order k in PGL(2, q) |
Jan 2 |
answered | A question about minimal simple group |
Dec 19 |
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Reference: Finite $p$-Groups
@Prof. A. Mann. As you have given many beautiful results on $p$-groups, I fasciate your book on $p$-group. I am very glad even if I know the content of the few chapter you have written. |
Dec 19 |
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Reference: Finite $p$-Groups
I am also interested with the book by A Mann who do many contribution to p-groups. |
Oct 3 |
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Number of Normal subgroups In a p-Group
About the minimality of normal subgroup, you can get this fact mentioned in the comment of Alexander Gruber following the answer of Nick Gill, from the paper by N. Blackburn, On a special class of p-groups. By the way, the above paper is an important paper for the theory of p-group |
Oct 2 |
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Number of Normal subgroups In a p-Group
@Nick: Let $G$ be a $p$-group of order $p^n$, and S the set of all subgroups of order $p^m$. Let $P \in S$. Then $P$ can acts on $S$ by conjugation. By counting the orbits of this action, we see $|S|$ congruent to 1. This trick is use to prove Sylow theorem by someone. So in some book I can not find, I think this is also called Sylow theorem. |
Oct 2 |
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Number of Normal subgroups In a p-Group
From Sylow Theorem, we see that the number of subgroups of a given order in a finite $p$-group is congruent to 1 mod $p$. Maybe Alexander means this. |