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(a) Find an example of groups G, H, K with K H and H G but K G.
(b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that every characteristic subgroup is normal.
(c) Show that if K ⊆ H ⊆ G, K is characteristic in H and H is characteristic in G then K is characteristic in G.
(d) Show that Dn(G) is normal in all of G not just in Dn-1(G).
(e) Conclude that G is solvable i it has a subnormal series in which each quotient is abelian and each group in the series is normal in all of G.
If G is a group, an automorphism of the form is called an inner automorphism. An automorphism not of this form is called outer.
The aim of the following questions is to show that all the automorphisms of Sn are inner, except for S6 which does have an outer automorphism.
The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi
A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, both head and tail have appeared , and B be the event at most one tail i
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E - L - P - S : Has the title of this section stumped you? Children, similarly, don't understand new symbols that are thrust upon them without giving them an adequate grounding. Y
If 7sin 2 ?+3cos 2 ? = 4, show that tan? = 1/√3 . Ans: If 7 Sin 2 ? + 3 Cos 2 ? = 4 S.T. Tan? 1/√3 7 Sin 2 ? + 3 Cos 2 ? = 4 (Sin 2 ? + Cos 2 ?)
Solving Trig Equations with Calculators, Part II : Since this document is also being prepared for viewing on the web we split this section into two parts to keep the size of the
functions f&g on R to R such that f=\g but fog=gof
Is there any assignment work available for mathematics?
whats 100 + 90 - 6
I need help converting my project fractions into 1
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