Equation 677 Database

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Magma 7ea77c1b4fec…

magma 7ea77c1b4fec
Size
321
Isomorphism class hash
7ea77c1b4fecbba79577dd128c0133f1d285beeb226913030d126040e66bf0c9
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 22:32:58
Display reorder
300,88,155,75,5,66,89,156,76,3,67,77,90,4,68,157,87,78,158,0,65,85,79,159,2,63,86,227,231,1,64,153,73,11,80,58,154,74,9,81,59,152,72,10,82,60,69,149,7,83,61,70,150,8,84,62,71,151,6,228,226,305,314,303,308,288,291,290,246,289,292,294,295,247,293,299,296,248,297,298,285,286,287,249,284,276,278,279,250,277,280,282,283,251,281,255,254,244,252,253,258,259,245,256,257,263,262,243,260,261,266,267,240,265,264,270,271,241,269,268,275,274,242,273,272,319,320,317,318,163,179,34,15,235,232,180,35,16,190,33,164,17,191,181,162,30,178,14,189,160,31,176,12,187,161,32,177,13,188,170,25,21,167,182,171,26,22,168,183,172,24,23,169,184,28,173,20,166,185,29,174,18,165,186,27,175,19,233,234,306,301,313,311,211,42,146,91,195,212,40,147,92,196,148,213,93,197,41,210,145,38,94,194,208,143,39,95,192,209,144,37,96,193,46,138,97,203,200,44,139,98,204,201,45,140,99,205,202,141,36,100,206,236,142,224,101,237,198,230,43,102,207,199,316,310,307,302,219,54,111,133,116,217,52,109,134,117,110,218,132,115,53,215,114,57,136,119,216,112,55,137,120,214,113,56,135,118,49,106,131,223,122,50,107,129,221,123,51,108,130,222,121,105,48,127,239,125,103,225,128,238,229,104,47,126,220,124,304,309,312,315 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#59c0dab3d55e83047c113809dcb6925b23956e0c747f2365bb6fbba97ebd5493, 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 22:32:59 · history