A genius? I just love studying.

Chapter 86: Enlightenment (7th update)

At ten o'clock in the morning, Fang Wen raised his head from the messy pile of draft papers, looked at the bright sunshine outside the window, and burst into laughter.

Then quickly, he picked up the computer and ran to the teaching and research office.

At this point, everyone has already arrived at the teaching and research department, either studying or writing papers. Choosing to be a graduate or doctoral student in the Department of Mathematics means that you are destined to have no chance to have fun.

"Fang Wen?"

"Did you go to practice Taoism last night?"

Wang Jianwei stared at Fang Wen who appeared at the door of the teaching and research office with wide eyes, and couldn't believe that this was the junior brother he remembered.

At this time, Fang Wen's hair was like messy dead grass, his face was as pale as paper, his eyes were bloodshot, and there were deep bruises under his eyes, as if he had been hit hard twice. His eye bags were swollen, and he looked like all his yang energy had been sucked dry.

But strangely, there was light in his bloodshot eyes!
"Big Brother, please help me look at the paper!"

Fang Wen didn't even have time to send the file. He just put his personal notebook on Wang Jianwei's desk and turned the screen to face Wang Jianwei.

"I say, you don't have to be too anxious. You won't graduate until next year, so you still have plenty of time to write your thesis!"

Wang Jianwei rarely comforted Fang Wen, as he was a little worried about Fang Wen's condition.

There are quite a few vicious incidents in the Department of Mathematics, especially among those studying theoretical mathematics.

"I'm fine!"

"I've never felt so energetic!"

Fang Wen's eyes lit up as he spoke excitedly.

But this appearance made the seniors in the teaching and research department even more worried.

Wang Jianwei thought it would be better not to provoke his junior brother at this time, so he lowered his head to look at his junior brother's computer screen.

It was still the same paper as before. Just as Wang Jianwei expected, what earth-shaking changes could be made in one night? If it could be done, it would have been done long ago.

Scroll the mouse wheel until you reach Summary.

In this paper, we propose a unified decomposition theorem for the structure of automorphism groups of finite p-groups (where p is an odd prime number) with a unique cyclic maximal subgroup. By constructing an explicit representation for such a group, G = a, b|a^{p^{n-1}}=1, b^p = a^{kp^{n-2}}, [a, b] = a^{lp^{n-2}}, we prove that its automorphism group, Aut(G), can be decomposed into the semidirect product GL(1, Z/pZ)Hom(G/Φ(G), Φ(G)), where Φ(G) is a Frattini subgroup. This result overcomes the bottleneck of traditional matrix representations, which are limited by high-dimensional computations, reducing the complexity from O(p^{2n}) to O(p^n).

The summary has been slightly modified, but overall it remains the same as before.

"what!"

But soon, Wang Jianwei let out a light exclamation and his expression became serious.

He discovered something new in the core innovations below the abstract!
"Have you completed the completeness of the Frattini quotient group G/Φ(G)?"

Wang Jianwei was also somewhat excited. He knew that when Lao Liu gave Fang Wen this suggestion, he meant it to motivate Fang Wen to some extent, and he did not think that Fang Wen could actually do it.

If Fang Wen really succeeded, then his late night would not have been in vain.

Fang Wen shook his head, "If it's just this little thing, it won't take me a whole night!"

Wang Jianwei rolled his eyes. He really got caught by this guy's pretense. But now he was really curious about what amazing things Fang Wen's family had made in one night.

He quickly slid the mouse and skipped over the research background and target chapters. He had always been Fang Wen's mentor. Although he didn't know all of these by heart, he was familiar with them.

Come to the proof chapter.

Soon, he saw Fang Wen's proof.

By introducing Blackburn's theorem to restrict mappings, we prove that the images of all quotient group layers of automorphisms fall within the GL(1, p) subgroup. We then construct an explicit formula for lifting and verify the compatibility of the lifting preservation relation. Wang Jianwei's eyes lit up, "That's right!"

After just a quick glance at the proof, Wang Jianwei knew that there was nothing wrong with the idea.

"Brother, why not continue reading!"

Fang Wen was also very proud. At this moment, he felt that all his efforts were worth it.

The coefficient compatibility loophole of the matrix representation in step 2, the identity assumption of the homomorphic kernel and the hom group in step 3, the unnatural splitting problem of the semidirect product structure in step 4...

Good guy!
Seeing the proofs one after another, Wang Jianwei's eyes widened.

He had discovered some of these problems before, but this was just a graduate thesis after all, and some minor flaws were allowed. It was not to be published in a journal, so he did not raise them. Of course, the most important thing was that he thought Fang Wen would not be able to solve them even if he raised them. As Fang Wen's senior for so many years, he understood Fang Wen's level.

But now, Fang Wen has proven not only some of the minor problems he had discovered before, but also the problems he had not discovered before.

After another look, he couldn't find the problem.

It’s not that the quality of this paper is really that high. The upper limit of the problem studied in this paper itself is just that. Even if Fang Wen comes up with some new ideas, that’s all.

However, this paper's research on this issue is very complete and can definitely be considered a qualified graduate thesis.

"Congratulations!"

After reading the proof of the paper in one breath, Wang Jianwei looked up and sincerely congratulated Fang Wen, "Could it be that you dreamed of an immortal, and that an immortal touched your head and opened up your Ren and Du meridians?"

"You can say that!"

Fang Wen also showed a bright smile on his face!

He originally thought that he might have to delay his graduation, but unexpectedly, things turned out well and he actually completed his graduation thesis before the start of his third year of graduate school!
"Thank you, Senior Brother. I'll send the paper to Professor Liu first. I'll treat everyone to cross-legged beef at noon!"

After saying that, he turned to the other senior brothers and sisters, and said to them, "Everyone go!"

"Yes, yes, yes!"

The little apprentice sister cheered, then blinked her big eyes at Fang Wen, "But brother, I want to eat roasted bread!"

"arrange!"

Fang Wen agreed without hesitation. His junior sister was not from Chengdu, and the appeal of roast meat to outsiders like them was no less than that of hot pot.

In fact, due to the popularity of hot pot, roasters have become even more attractive.

People feel refreshed when they are happy. After staying up all night, Fang Wen was full of energy and not sleepy at all. He returned to his seat with his computer and started editing emails.

"Come on, you can eat cross-legged beef anytime. Just go back to bed after sending the email."

Wang Jianwei was still quite pleased. Even though he was always at odds with Fang Wen, as the senior brother in the laboratory, it was not an exaggeration to say that Fang Wen was the one who brought up the new kid. Seeing that the little guy he brought up could graduate successfully, he naturally felt a great sense of accomplishment.

"Brother, send me your paper so I can study it!"

As soon as she returned to her seat, the little junior sister looked at Fang Wen's screen curiously, her eyes full of envy.

Not only the junior sister, but even the seniors in the teaching and research department looked at her with envy, as they had not yet finished their graduation thesis.

"no problem!"

Fang Wen tapped the keyboard quickly, and then copied the email to his junior sister when sending it.

(End of this chapter)