Equation 677 Database

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Magma 469a92ff6888…

magma 469a92ff6888
Size
321
Isomorphism class hash
469a92ff68881eba667b3286df4d25c01bc8328978df087d92ea1b291f55d62f
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 22:36:51
Display reorder
300,18,128,82,142,214,19,215,126,83,143,127,213,20,81,141,21,131,210,78,138,22,129,211,79,139,23,130,212,80,140,205,123,16,73,133,206,124,17,74,134,204,125,15,72,132,122,208,12,76,136,120,209,13,77,137,121,207,14,75,135,301,304,305,309,40,294,293,292,295,41,298,299,296,297,290,291,39,289,288,36,279,278,277,276,37,282,283,280,281,38,286,287,284,285,258,259,46,256,257,263,262,47,260,261,254,255,45,252,253,271,270,42,268,269,275,274,43,273,272,267,266,44,264,265,320,319,318,317,11,166,188,176,202,9,203,167,186,174,165,201,10,187,175,7,162,198,191,179,8,163,199,189,177,6,164,200,190,178,193,157,2,183,171,194,158,1,184,172,192,156,0,185,173,160,196,5,182,170,161,197,3,180,168,159,195,4,181,169,308,307,315,316,115,226,106,92,154,116,155,227,107,90,225,153,114,105,91,118,222,150,102,95,119,223,151,103,93,117,224,152,104,94,145,217,113,97,87,146,218,111,98,88,144,216,112,96,89,220,148,109,100,86,221,149,110,101,84,219,147,108,99,85,303,310,302,306,30,249,55,248,64,31,65,250,56,251,247,63,32,54,246,33,241,60,58,240,34,243,61,59,242,35,244,62,57,245,70,231,28,53,230,71,233,29,51,232,69,228,27,52,229,237,66,24,49,236,238,67,25,50,239,235,68,26,48,234,313,312,311,314 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#62d5cd0053185ccae094f96e2ae535daccc2dacd55a9f14470e4ff2a7e2e534c, 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 22:36:51 · history