Measure the height of a stack of 50 pennies (in centimeters).

1. Measure the height of a stack of 50 pennies (in centimeters). 2.Convert the height of the stack of pennies into meters 3.Calculate how many pennies would be needed to make a tower 1 billion meters tall. Give answer in both standard calculation and in scientific notation.

Group Theory, Computing number of odd order subgroups

Question: Let G be a group of order 2k , that contains a cyclic subgroup of order k, where k is odd. Determine a formula to compute the number of subgroups of G that are of odd order.

Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero.

Problem 1: Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero. Problem 2: prove that no pair of the following groups of order 8, I8; I4 x I2; I2 x I2; D8; Q, are isomorphic.

Algebraic Structures

Problem #1 Prove that Aut(V)= (S3)and that Aut(S3)= S3. Problem #2 If H and K are normal subgroups of a group G with HK = G. Prove that G/(H n K) = (G/H) x (G/K).

Algebraic Structures

The problem I do need help in this attached sheet is problem # 264. Thanks in advance.