Questions tagged [groups]

Maria Sun Oct 27 2024 | 7 answers 1741

I would like to know who are the users of Combined Heat and Power (CHP). I'm interested in understanding the range of customers or entities that typically adopt this technology for their energy needs.

henry_miller_astronomer Thu Sep 19 2024 | 7 answers 1608

Could you please elaborate on the concept of "free groups" and "abelian groups" and explain why the question "Are free groups abelian?" arises in the context of algebra and group theory? Are there specific properties of free groups and abelian groups that lead to this inquiry, and if so, what are they? Additionally, could you provide a concise yet comprehensive answer to the question, considering the fundamental definitions and properties of these groups?

EnchantedDreams Tue Sep 17 2024 | 7 answers 1204

I'm curious, what alternative terminology exists for an abelian group? Is there another name commonly used in the realm of mathematics or abstract algebra that refers to this specific type of group, where the operation is commutative and the order of the elements does not affect the result of the operation? I'm eager to learn if there's a synonym or alternate phrase that could be used interchangeably to describe an abelian group.

SilenceStorm Mon Sep 16 2024 | 5 answers 892

Could you clarify for me if all abelian groups are necessarily simple? I understand that an abelian group possesses the property of commutativity, meaning that the order in which elements are combined does not affect the result. However, I'm unsure if this characteristic alone implies that such groups are simple, i.e., having no non-trivial proper subgroups. Could you elaborate on the relationship between the commutative nature of abelian groups and their simplicity, or perhaps provide an example that illustrates whether or not all abelian groups are simple?

CosmicDream Mon Sep 16 2024 | 5 answers 1165

Could you please elaborate on the concept of "abelian groups" and their relation to the term "solvable"? Are you referring to the mathematical property of abelian groups being solvable in the sense of group theory, where a group is considered solvable if it has a composition series whose factors are all abelian groups? Or is there another interpretation of "solvable" that you have in mind when asking about abelian groups? Clarifying this would help me provide a more accurate and relevant answer to your question.