In the context of group theory, a **Carter subgroup** is a specific type of subgroup associated with a finite group, particularly in the study of nilpotent and solvable groups. Specifically, a Carter subgroup is defined as follows: - It is a subgroup that is the intersection of all Sylow subgroups corresponding to its normalizer in the group.

A **C-normal subgroup** is a concept from group theory, a branch of mathematics that studies the algebraic structures known as groups. A subgroup \( N \) of a group \( G \) is termed a **C-normal subgroup** if it satisfies certain conditions related to its normality.

In group theory, an **abnormal subgroup** is a specific type of subgroup that captures certain properties related to the structure of the group. A subgroup \( H \) of a group \( G \) is called **abnormal** if it satisfies the following condition: For every \( g \in G \), if \( gH \) (the left coset of \( H \) in \( G \)) intersects with \( H \) non-trivially (i.e.

ZhuZhu Pets are a brand of electronic toy pets that were created by a company called Cepia, LLC. They were first released in 2009 and quickly became a popular toy among children. The toys are small, interactive hamsters that move around on their own, make various sounds, and respond to touch. Each ZhuZhu Pet has its own personality and name, contributing to their appeal.

Yoshikitty is a character created as a collaboration between Yoshiki, the renowned Japanese musician, composer, and co-founder of the influential rock band X Japan, and Sanrio, the company behind Hello Kitty and other popular characters. Yoshikitty is essentially a fusion of Yoshiki and Hello Kitty, combining elements of both in a cute, whimsical design.

Greg Mankiw is an American economist and professor known for his work in macroeconomics, public policy, and economic education. He is a professor at Harvard University and has served as the Chairman of the Council of Economic Advisers under President George W. Bush. Mankiw is also well-known for his widely used textbook "Principles of Economics," which has been influential in teaching economics to students around the world.

George O. Abell was an American astronomer best known for his work in the field of galaxy clusters and for his contributions to observational cosmology. He was born on March 1, 1927, and passed away on July 7, 1983. Abell is particularly noted for creating the Abell catalog of rich clusters of galaxies, which is a significant resource for astronomers studying the large-scale structure of the universe.

Ed Krupp is an American astronomer known for his work related to celestial and planetary sciences. He is particularly recognized for his role as the Director of the Griffith Observatory in Los Angeles, California. Under his leadership, the observatory has become a significant educational and public outreach institution that fosters interest in astronomy and space science. Krupp has also contributed to various scientific publications and has been involved in numerous community programs aimed at enhancing public understanding of astronomy.

Uglydoll is a brand and franchise that features a line of plush toys known for their distinctive, quirky designs and playful characters. Created in 2001 by David Horvath and Sun-Min Kim, Uglydoll originated from a handmade toy that Horvath designed for Kim. The characters are characterized by their imperfections, unique shapes, and bright colors, often embodying themes of acceptance, individuality, and positivity in the face of flaws.

YooHoo & Friends is a franchise focused on a line of plush toys, animated series, and other media featuring a group of colorful and adorable animal characters. The characters in YooHoo & Friends are inspired by real-life animals that are endangered or threatened, and they are designed to promote awareness about wildlife conservation and environmental issues.

"Yappin' Yinzers" is likely a reference to a podcast or media project that features discussions and commentary on topics related to Pittsburgh culture, sports, and local events, often using the Pittsburgh dialect and slang. The term "yinz" is a common colloquialism used in the Pittsburgh area similar to "y'all" in the South.

Ty Classic is a specific line of plush toys created by the company Ty Inc., which is best known for its Beanie Babies and other stuffed animals. The Ty Classic collection typically features larger, more detailed, and high-quality plush toys, often designed with unique characters and special features. These toys are made with soft materials and are often characterized by their expressive faces and vibrant colors. The Ty Classic line includes a variety of animals and characters, appealing to children and collectors alike.

A teddy bear is a soft, stuffed toy in the shape of a bear, commonly used as a children's toy or comfort object. Typically made from plush fabric and filled with materials like polyester fiber or cotton, teddy bears come in various sizes, colors, and designs. They often have button or embroidered eyes and a stitched nose and mouth. The teddy bear has become an iconic symbol of childhood and comfort, often associated with warmth, love, and friendship.

In group theory, a **subnormal subgroup** is a specific type of subgroup that has a particular relationship with the larger group it is part of.

A semipermutable subgroup is a concept in the field of group theory, particularly in the study of group extensions and solvable groups. A subgroup \( H \) of a group \( G \) is called **semipermutable** if for every normal subgroup \( N \) of \( G \) such that \( N \) is a subset of \( H \), the subgroup \( H \) permutes with \( N \) in \( G \).

A **quasinormal subgroup** is a concept in group theory, a branch of abstract algebra. A subgroup \( H \) of a group \( G \) is said to be quasinormal if it is permutable with every subgroup of \( G \).

A sock monkey is a type of stuffed toy that is traditionally made from a socks, typically a red-heeled sock. The design is characterized by its long limbs, a tail, and a distinctive monkey face, often with button eyes and a stitched mouth. Sock monkeys originated in the United States in the early 20th century and became popular as a children's toy. They are often associated with nostalgia and Americana.

Sing-a-ma-jigs are interactive stuffed toys that were popularized in the early 2010s. They are known for their unique ability to sing songs and harmonize with each other when activated. Each Sing-a-ma-jig has a quirky appearance, featuring a wide mouth and colorful designs that appeal to children.

Puffkins is a brand of plush toys that were popular in the 1990s. The toys are characterized by their soft, squishy bodies and distinctive design, often resembling cute animals or fantasy creatures. Each Puffkin typically features large, expressive eyes, colorful fabric, and a unique personality. Puffkins were produced by the toy company Applause, which was known for creating a variety of collectible plush items.

Pillow Pets is a brand of plush toys that can be transformed from a stuffed animal into a pillow. These products are known for their soft, cuddly design and versatility, appealing primarily to children. The animals are made of high-quality materials and come in various shapes and characters, ranging from popular animals to licensed characters from movies and television shows. When folded, they function as a decorative pillow, and when unfolded, they serve as a cozy plush toy.