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I am an ex assistant-professor of mathematics at the Univ. of Amsterdam, with specialization in group theory and representation theory of groups. I work for IBM, though not in research.


May
15
awarded  Caucus
May
7
comment Which finite groups are the group of units of some ring?
Jack, thanks for this clarification! I read Gilmer's paper a long time ago and wasn't aware of Pearson-Schneider's.
May
7
answered Which finite groups are the group of units of some ring?
May
6
answered Good book on representation theory after reading Rotman
May
6
revised Martin Isaacs's exercise 3.7 (character theory of finite groups)
edited body
May
6
answered Applications of Character Theory
May
6
answered Applications of Character Theory
May
3
comment Properties which are constant on conjugacy classes of a group
I used to be a professional group theorist for more than ten years ...
May
3
comment Showing that if $N \le G$ is finite minimal normal and every simple homomorphic image is abelian, then N is elementary abelian
Hint: A minimal normal subgroup is characteristically simple, so if it is finite then it is a product of isomorphic simple groups.
May
3
answered if $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
Apr
26
comment If $ G $ has no non-trivial automorphism, then $ G $ is abelian and $ g^2 = e $ for all $ g \in G $ .
Good point! And yes I am an AC believer :-)
Apr
25
answered If $ G $ has no non-trivial automorphism, then $ G $ is abelian and $ g^2 = e $ for all $ g \in G $ .
Apr
25
comment If H is a p-group, the order of any H-orbit is a power of p.
By the way, it is not too hard to show that the orbit size of $K$ actually equals $[H:H\cap K]$ ($= [K:H\cap K]$)
Apr
25
answered If H is a p-group, the order of any H-orbit is a power of p.
Apr
24
answered Simplifying $\sin(2\tan^{-1} x)$
Apr
24
answered Properties which are constant on conjugacy classes of a group
Apr
24
comment Need to show that order of orbits under group action is non-trivial and intersection of two p-groups is a proper subgroup
If $P_1 \cap P_i = P_1$, then $P_1 \subset P_i$ and since they have equal order it follows that $P_1 = P_i$, a contradiction with your choices. BTW: your sentence "through some probably irrelevant logic" refers to some essential and typical Sylow p-group theory, and is not so irrelevant as you might think.
Apr
22
revised There exist Sylow subgroups $P$ and $Q$ for which $[P:P \cap Q]=[Q : P \cap Q] = p$.
replaced conjunction by conjugation
Apr
14
awarded  Yearling
Apr
5
comment Show that $N$ is a normal subgroup in $G$ when $N$ is the intersection of normal subgroups in $G$
Yes, good point, some texts use that