User tom - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T03:14:17Z http://mathoverflow.net/feeds/user/27449 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/125515/a-group-with-all-sylow-p-subgroups-cyclic a group with all sylow p subgroups cyclic Tom 2013-03-25T09:16:38Z 2013-03-26T00:06:38Z <p>If there exist a non cyclic group $G$ with all sylow $p$subgroups cyclic,and the normal $p_1$-complement $M$ for $G$ is cyclic,here $p_1$ is the smallest factor of $|G|$?And when does it always exist?</p> http://mathoverflow.net/questions/117237/the-number-of-odd-sylow-numbers-in-a-non-abelian-simple-group the number of odd sylow numbers in a non-abelian simple group Tom 2012-12-26T09:19:09Z 2012-12-26T09:19:09Z <p>Let $G$ be a non-abelian simple group.Is there exist a positive integer number $k$ such that there are at most $k$ odd sylow numbers in $G$?</p> http://mathoverflow.net/questions/110609/a-simple-question-about-the-center-of-a-finite-group A simple question about the center of a finite group Tom 2012-10-25T02:29:37Z 2012-10-25T09:22:21Z <p>Let $G$ be a finite group. $N$ a normal subgroup of $G$ and $K$ a characteristic subgroup of $N$: $$K \text{ char } N \triangleleft G.$$ If $Z(G/N)=1$ and $Z(G)=1$, does it follow that $Z(G/K)=1$?</p> http://mathoverflow.net/questions/110315/question-on-the-equal-sylow-number-in-finite-non-abelian-simple-group Question on the equal Sylow number in finite non-abelian simple group Tom 2012-10-22T10:35:24Z 2012-10-22T13:50:05Z <p>let $G$ be a finite non-abelian simple group.If there exist $p$ and $q$ which are different prime numbers of $|G|$ such that $n_p(G)=n_q(G)$?</p> http://mathoverflow.net/questions/125515/a-group-with-all-sylow-p-subgroups-cyclic/125517#125517 Comment by Tom Tom 2013-03-26T01:26:22Z 2013-03-26T01:26:22Z @Nick,Mark:Is there a classification of Sylow-cyclic groups in which cases they are cyclic or noncyclic? http://mathoverflow.net/questions/125515/a-group-with-all-sylow-p-subgroups-cyclic/125573#125573 Comment by Tom Tom 2013-03-26T01:17:50Z 2013-03-26T01:17:50Z @Geoff:If both the Sylow $p$subgroup $P$ and the normal $p-$complement are cyclic,here $p$ is the smallest prime divisor of $|G|$,if we can get $C_G(P)=P$ or what will happen to $G$?And in what cases $G$ can be noncyclic? http://mathoverflow.net/questions/110609/a-simple-question-about-the-center-of-a-finite-group Comment by Tom Tom 2012-10-25T05:15:01Z 2012-10-25T05:15:01Z Thanks a lot,however,if we add an other condition $1&lt;$K&lt;$H&lt;G$.May you get another counter-example. http://mathoverflow.net/questions/110609/a-simple-question-about-the-center-of-a-finite-group/110610#110610 Comment by Tom Tom 2012-10-25T04:35:29Z 2012-10-25T04:35:29Z I am sorry.It is not the case.It is $K$char$N\triangleleft G$. Thank you all the same. http://mathoverflow.net/questions/110609/a-simple-question-about-the-center-of-a-finite-group Comment by Tom Tom 2012-10-25T04:03:02Z 2012-10-25T04:03:02Z Sorry,I have corrected it.$K$char$N$. http://mathoverflow.net/questions/110315/question-on-the-equal-sylow-number-in-finite-non-abelian-simple-group/110320#110320 Comment by Tom Tom 2012-10-23T10:48:02Z 2012-10-23T10:48:02Z If $G\in A_n$ is a $K_m$ group,then I know that there are $m$ different sylow numbers about $G$. http://mathoverflow.net/questions/110315/question-on-the-equal-sylow-number-in-finite-non-abelian-simple-group Comment by Tom Tom 2012-10-23T04:55:52Z 2012-10-23T04:55:52Z $n_2(A_5)=5,n_3(A_5)=10$and$n_5(A_5)=6$ http://mathoverflow.net/questions/110315/question-on-the-equal-sylow-number-in-finite-non-abelian-simple-group/110320#110320 Comment by Tom Tom 2012-10-23T04:47:53Z 2012-10-23T04:47:53Z Then how about $A_n$(Alternating groups)