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In mathematics, a group is a set equipped with a binary operation that is associative, has an identity element, and is such that every element has an inverse. These three conditions, called group axioms, hold for number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The formulation of the axioms is, however, detached from the concrete nature of the group and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of many mathematical objects. The ubiquity of groups in numerous areas—both within and outside mathematics—makes them a central organizing principle of contemporary mathematics.Groups arise naturally in geometry for the study of symmetries and geometric transformations: the symmetries of an object form a group, called the symmetry group of the object, and the transformations of a given type form generally a group. These examples were at the origin of the concept of group (together with Galois groups). Lie groups arise as symmetry groups in geometry but appear also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting of the symmetries of spacetime in special relativity. Point groups describe symmetry in molecular chemistry.
The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s, who introduced the term group (groupe, in French) for the symmetry group of the roots of an equation, now called a Galois group. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become an active area in group theory.

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  1. T

    Hi guy introducing myself to the group

    Just getting back into heating and plumbing after a break at university. Looking forward to contributing. Cheers Tim
  2. A

    Mixing group conflict with Zone valve?

    hi All, can someone help me clarify following issue? is there possibility when room stat calls for heat (UFH system), it opens the zone valve, runs the manifold pump and turns on the boiler but the mixing group does not start mixing the incoming hot water and does not allow the incoming hot...
  3. A

    Spencer Group Plumbing & Heating Ltd

    Alex_96 submitted a business listing in the plumbers directory: Spencer Group Plumbing & Heating Ltd - Plumbing and Heating Engineer In Wolverhampton Checkout this business listing... - Please leave a review for this company if you have used them before. You can add your own plumbing business...
  4. J

    Help me understand the specifications of an UFH mixing group

    Hello everyone, I have installed in my house an UFH system that consists of: Condensing boiler Hydraulic separator 4.5m3/hr UFH mixing group - TECEfloor – 7745 00 00 Manifold TECEfloor – 7731 00 xx The circuits are laid as follows: Zone 1 3 circuits 80m each 10 cm spacing Zone 2 1 circuit...
  5. Dan

    How to deal with offensive posts - Never reply to them, Always report them

    If you find a post that is offensive to you, or you think it is offensive to somebody else, then please report the post and do not reply to it. When you reply to a post that we might be pulling for offensive content, we then need to go and check your replies, and see if anybody has quoted the...
  6. Lou

    Grafton group sells Plumbase

    I just read this about @Plumbase being sold. Did anyone else hear about it? HISTORIC PLUMBING AND HEATING BUSINESS SOLD IN £66M DEAL 2 Oct 2019 Midlands Deals Jon Robinson A specialist UK plumbing and heating business, which was founded more than 155 years ago, has been sold in a deal worth...
  7. D

    What’s app group for engineers !!!

    Anyone been added to a whats app group for “engineers” ?????? Added today to my first and no joke, one of the first posts was “is this ok ????” Can’t add a picture to this but it was a picture of a hob with the gas line running down the center of wall immediately behind it. Second question...
  8. T

    New Member to this group

    Thanks for adding me to the group. Hope I can learn and share with members over time
  9. L

    Emergency Response Group (ERG)

    Anyone been called by these scammers to do work for them? Used to be knows as LOM based out of Essex: Check this - not good! Emergencyresponsegroup is rated "Bad" with 0.4 / 10 on Trustpilot
  10. P

    Group Project - 2 Storey sustainable building accommodating 200 staff.

    Hi all, I am working on a group project at my university, which consists of designing a building to accommodate 200 members of staff. This involves designing the utilities. Below are some of the things that I have accounted for in the design in the hope that may be some of you with...
  11. S

    Beware of emergency response group westcliff

    hi a word of warning about a company called emergency response group / emergency repair group., anyone who has worked for them or has called them for a repair beware myself and hundreds of other people have been conned from them, they charge extortionate amounts and make it impossible for you...
  12. N

    Is your home heated up with a heat pump?

    Than you are the one we are searching for. Please participate in our Survey, let us know your opinion about your heat pump and get member in our Experience Group. Within the Workshop, which is aligned by one of the biggest heat pump manufacturer, you can discuss the advantages and disadvantages...
  13. Dan

    New Facebook Group - Trade Talk

    https://www.************/groups/214225459029066 Get yourself over there. :)
  14. A

    Anyone bought a van from arrow auto group in Essex?

    Hi guys looking at getting a van and these guys have some reasonably priced vans. I want to get one so I can start getting out and about doing motocross again. Anyone ever bought from them before?, long shot I know. Arrow Auto Group - Home Page of Arrow
  15. C

    caleffi pressure reducing valve/inlet group

    Does any one no if you can adjust the pressure reducing valve on these and if so how? thanks :)
  16. SimonG

    Facebook Oil Group

    Well s only a matter of time before it went the same way as the others. Too many clever cnuts, too eager to extract the urine rather than ignore or help.
  17. S

    Gas Engineer required in Swindon area, 30k + dependant on experiance

    Smallheating company (10 engineers) require another engineer join friendly team Predominately gas maintenance works but some occasional plumbing Further training in areas if needed Local work for 30yrs established company Everything provided Quality of workmanship is our no1 priority Ring...
  18. S

    Gas Engineer required in Swindon area, 30k + dependant on experiance

    Small heating company (10 engineers) require another engineer join friendly team Predominately gas maintenance works but some occasional plumbing Further training in areas if needed Local work for 30yrs established company Everything provided Quality of workmanship is our no1 priority Ring...
  19. W

    What the hells goin off with your FB group.

    This forum is mustard always has been and always will. But yer facebook thing is has got some right self righteous nasty pieces of work on it. It's like a massive arsey pee'ing contest.
  20. MarkAqua

    Gas engineering, heating & plumbing group. Facebook.

    Jesus Christ, What is everyone's problem on there? Everyone just slaughters each other! I think I've been on there for 2-3 week and that's enough. i'm off tonight lol.
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