Nicky Hekster

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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.

	2,677 reputation	bio	website	linkedin.com/profile/…	visits	member for	2 years, 1 month
413 badges		location			seen	7 hours ago

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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