Equation 677 Database

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Magma aa47139b7a69…

magma aa47139b7a69
Size
321
Isomorphism class hash
aa47139b7a69f3ddb521078b23a64008cebf125ec035c269c2316c121251f84a
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 22:50:13
Display reorder
300,191,9,162,155,107,187,10,163,153,105,189,11,164,154,106,8,183,165,151,103,6,185,166,152,104,7,181,167,150,102,172,1,160,146,98,169,0,161,144,96,171,2,159,145,97,3,178,156,149,101,4,174,157,147,99,5,176,158,148,100,307,301,308,303,299,17,297,296,298,291,15,288,289,290,295,16,293,292,294,13,283,281,280,282,14,287,285,284,286,12,279,276,277,278,263,23,261,260,262,255,21,253,252,254,259,22,257,256,258,19,275,273,272,274,20,267,264,265,266,18,271,268,269,270,318,320,319,317,250,58,251,85,82,247,59,246,86,83,248,57,249,84,81,54,242,243,88,78,55,244,245,89,79,56,241,240,87,80,232,49,233,91,73,228,50,229,92,74,230,48,231,90,72,52,238,239,94,76,53,235,234,95,77,51,237,236,93,75,313,314,311,312,199,129,213,227,139,200,130,214,225,140,198,131,215,226,138,128,202,212,223,142,126,203,210,224,143,127,201,211,222,141,197,120,204,218,137,195,121,205,216,135,196,122,206,217,136,123,193,207,221,133,124,194,208,219,134,125,192,209,220,132,310,304,305,302,27,61,190,37,113,28,62,186,38,111,29,60,188,36,112,64,26,182,40,109,65,24,184,41,110,63,25,180,39,108,33,67,173,43,119,34,68,168,44,117,35,66,170,42,118,70,32,179,46,115,71,30,175,47,116,69,31,177,45,114,306,316,315,309 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#b42b2593cdf495fd739236f86f5dbe699df6ba394eb7d6a8f934bf0cd7c90649, 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 22:50:14 · history