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I am struggling in the math part and understanding the cincept

 
 

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7.I’m struggling to start the questions in these photos. In the first photo’s question, I”m not sure how to ...

sure how to tell which rules to use and where to go from there. And In the last photo, I am specifically struggling with questions 29, 45, and 53.
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8.Hello there! I'm struggling with group solubility/solvability, Sylow subgroups, and nilpotency (university maths). I would like some assistance as soon ...

ersity maths). I would like some assistance as soon as possible (in the next few hours), so if you are unavailable, I would love it if another tutor could help. These are the questions that are similar to, but are not exactly the ones I am struggling with. Solving these would give me a better chance of solving my assignment. I don't know where to begin with these: Provide a non-solvable finite group G with solvable subgroups L, K, M such that G = LK = LM, M \neq K , and show that it fits the criteria. ///// Define G, a finite p -group, such that G isn't abelian. Let K \le G such that |G:K| = p , where K is abelian. Prove that there are either 1 or p + 1 such abelian subgroups, and if there are p + 1 , then the index of Z(G) in G is p^2 ///// Define N normal subgroup, G finite group, O the intersection of all maximal subgroups of G . Prove that G = ON and N \cap O is nilpotent. ///// Define p a prime number, G a finite group, K a Sylow p -subgroup of G . Assume M \le K and g^{-1}Mg \le K , where g \in G . Prove that g = km for some k \in N_G(K) (normaliser of K in G ) and some m \in C_G(M) (centraliser of K in G)
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics