Recent questions tagged group-theory

3 votes
1 answer
122
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true?$x=e, \: y=e...
0 votes
1 answer
123
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of...
2 votes
3 answers
125
1 votes
1 answer
128
1 votes
1 answer
129
1-) 12-) 23-) 34-) 4
2 votes
2 answers
130
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
0 votes
0 answers
131
Is this monoid:Addition modulo (take mode using m) on the set of Integers (Z m)={0,1,2,3,4,…..m-1}i.e. For all a a (+ modulo using m) e = e (+ modulo using m) a...
2 votes
2 answers
132
0 votes
0 answers
134
0 votes
0 answers
137
Lets S1 and S2 be two algebric structure :S1 : {0,1,2,3,4,….,m-1},+m-1S2 : {0,1,2,3,4,….,m-2},+m-1+m is the addition modulo m. Which of the following are Groups ?
1 votes
1 answer
139
0 votes
0 answers
140
Number of non-isomorphic groups of order 10 = ?
0 votes
1 answer
142
reference:Roseni think two more abelian groups are possible .1 and 3 are given ,2 and 4 also exist .if i m wrong let me know ,thank you.
1 votes
2 answers
143
5 votes
1 answer
145
Suppose that $G$ is a cyclic group of order $10$ with generator $a\in G$.Order of $a^{8}$ is _______
2 votes
1 answer
146
If two elements of a group G satisfies $aba^{-1} = b^{2}$ for $b\neq e$ then which of the following is equal to $b^{32}$$A) a^{16}ba^{-16}$$B) a^{5}ba^{-5}$$C) ab^{16}a^{...
2 votes
2 answers
147
1 votes
1 answer
148
How many different non-isomorphic Abelian groups of order 16 are there?
1 votes
0 answers
149
1 votes
1 answer
150
Can Please anybody describe the concept of Isomorphic Groups with an example ? Reference to https://gateoverflow.in/1219/gate2007-21