- Method not allowed when using post request to create item in Sitecore 9
- Strong and Weak Dominance Table
- monerod v0.12.2.0 does not start on Linux because of “./monerod: error while loading shared libraries: libpcsclite.so.1”
- How to create more outputs?
- Smart computing into MS-DOS? Is it possible?
- Standard Mexican Spanish vs Standard Spain/European/Iberian/Castilian/Peninsular Spanish
- Is the Phrase “Sola Dea Fatum Novit” Proper Latin?
- Translating “Nocte volat caelī mediō”
- How is a map initialised in memory
- How can we implement a new opcode in the Ethereum Virtual Machine.
- Where the Smart Contract deployment charges goes?
- Using the Ethereum storage for document certification
- Transaction wont commit to a block if I send transaction that is signed by private key that is generated by ethereumjs-wallet
- if library do not have storage then what is motive of defining a mapping in structure and passing struct to functions in it?
- Error: The method shh_newSymKey does not exist/is not available
- How to concat different parameters type in one parameter (bytes) and extract them?
- Is it possible to run multiple Ganache nodes for private test network?
- Transaction execution failed. Gas requirement high
- Solidity: substitute for returns (strings[])
- Is there a way to auto-compile contracts with truffle?

# How to check if $\mathbb{Z}_n\setminus \{\bar{0}\}$ create a group (or not a group) with multiplication ? (with given n)

How to check if $\mathbb{Z}_n\setminus \{\bar{0}\} $ create a group with multiplication ? (with given n)

For example, if $\mathbb{Z}_{41}$ create a group with multiplication.

I aware that I need to prove 4 things:

Closure:

For all a, b in G, the result of the operation, a • b, is also in G.b[›]

Associativity:

For all a, b and c in G, (a • b) • c = a • (b • c).

Identity element:

There exists an element e in G such that, for every element a in G, the equation e • a = a • e = a holds. Such an element is unique (see below), and thus one speaks of the identity element.

Inverse element:

For each a in G, there exists an element b in G, commonly denoted $a^{-1}$, such that a • b = b • a = e, where e is the identity element.

But I have trouble applying modulo in this case. Please give me a formal example.