Which subgroups are normal

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Active Oldest Votes. Improve this answer. Jack Schmidt Jack Schmidt 10k 1 1 gold badge 39 39 silver badges 55 55 bronze badges. Thanks for the great answer! Perhaps link to the original revision of the question could be added. I mean, under which condition s for a group, one can find a Hamiltonian subgroup of it?

Thanks and sorry for asking after a long time ago. Gjergji Zaimi Gjergji Zaimi Francois Ziegler Francois Ziegler 28k 4 4 gold badges silver badges bronze badges.

Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. According to Kramer p. Normal subgroup is found in English in in An Introduction to the Theory of Groups of Finite Order by Harold Hilton: "Similarly, if every element of G transforms a subgroup H into itself, H is called a normal , self-conjugate , or invariant subgroup of G or 'a subgroup normal in G'.

Miller writes in Historical Introduction to Mathematical Literature , "In the newer subjects the tendency is especially strong to use different terms for the same concept. For instance, in the theory of groups the following seven terms have been used by various writers to denote a single concept: invariant subgroup, self-conjugate subgroup, normal divisor, monotypic subgroup, proper divisor, distinguished subgroup, autojug.

In Latin, "norma" means "set square" "triangle" , whose chief purpose is to draw a right angle or, more straightly, two adiacent right angles. Of course this is just my guess. Sign up to join this community.

The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why are normal subgroups called "normal"? Ask Question.