Equation 677 Database

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Magma 1eddc02f9bcc…

magma 1eddc02f9bcc
Size
321
Isomorphism class hash
1eddc02f9bccff3c23bb6e41e462b7da02164923ebcbaf2848f1f41f98e81a73
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 22:50:49
Display reorder
300,34,40,182,106,171,35,172,41,183,107,42,170,33,181,105,43,31,174,233,217,44,32,175,184,244,248,208,206,173,108,38,180,169,45,104,39,178,167,46,102,37,179,168,47,103,177,36,165,48,100,232,207,166,49,101,176,239,247,209,216,312,314,304,315,3,283,282,281,280,4,284,287,286,285,279,277,5,278,276,295,2,292,294,293,299,1,296,298,297,290,291,0,289,288,9,274,272,275,273,10,266,265,267,264,11,270,269,271,268,258,8,256,259,257,262,6,260,263,261,254,7,252,255,253,320,317,319,318,70,132,160,148,204,214,237,246,161,149,131,12,69,159,231,225,73,13,163,151,134,71,14,164,152,162,133,72,15,150,76,158,29,130,147,74,156,30,128,145,75,157,28,129,146,154,78,26,224,230,155,77,27,127,144,153,241,238,223,229,302,311,310,307,17,189,88,113,55,18,56,190,86,114,188,54,16,87,112,192,20,58,84,116,193,21,59,85,117,83,191,19,57,115,23,81,53,235,111,205,79,211,186,219,22,80,52,187,110,82,25,51,234,245,215,236,210,249,218,242,24,50,185,109,301,313,305,316,93,199,139,64,122,94,123,197,140,65,198,121,92,138,63,195,89,125,142,67,196,90,126,143,68,141,194,91,124,66,98,137,120,203,62,99,136,119,201,61,97,228,222,202,213,135,95,220,251,212,227,243,221,250,240,226,96,118,200,60,306,308,303,309 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#b87a44718af64d04bd4c9a05b8565b67306fb6d5f63754d3fbad663d9bf67702, 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 22:50:50 · history