Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma ea6d95de891f…

magma ea6d95de891f
Size
321
Isomorphism class hash
ea6d95de891f903a02b966b04e201f46c74e6dc1c26e837cd2e923f57b74aa71
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:59:25
Display reorder
300,6,153,78,230,140,7,79,228,138,154,8,155,80,229,139,9,81,152,233,143,10,82,150,231,141,11,83,151,232,142,76,4,144,236,135,234,77,5,145,136,75,3,146,235,137,1,72,147,239,134,0,73,148,237,132,2,74,149,238,133,315,312,306,305,244,263,262,261,260,245,253,252,255,254,243,258,257,256,259,240,273,274,272,275,241,264,266,265,267,242,269,270,268,271,284,250,285,286,287,278,277,251,276,279,280,249,281,282,283,246,296,297,298,299,247,289,288,290,291,248,293,292,294,295,320,317,319,318,65,89,98,43,194,63,96,44,192,87,64,88,97,42,193,61,101,85,46,197,62,99,86,47,195,60,100,84,45,196,104,71,95,41,200,39,102,69,93,198,103,70,94,40,199,67,107,91,37,203,68,105,92,38,201,66,106,90,36,202,302,311,316,303,125,110,28,163,49,123,29,164,50,108,124,109,27,162,48,121,24,113,166,52,122,25,111,167,53,120,26,112,165,51,34,131,116,161,55,159,35,129,114,56,33,130,115,160,54,127,30,119,157,58,128,31,117,158,59,126,32,118,156,57,307,314,304,310,15,218,173,182,209,16,171,180,207,216,17,217,172,181,208,14,169,221,185,205,12,170,219,183,206,13,168,220,184,204,179,21,224,188,215,186,177,22,222,213,178,23,223,187,214,20,175,227,191,211,18,176,225,189,212,19,174,226,190,210,308,313,309,301 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, M = {60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:59:26 · history