Equation 677 Database

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Magma 05e62aee1c86…

magma 05e62aee1c86
Size
321
Isomorphism class hash
05e62aee1c86a291cae28c071ac1edac2871593ec16306b41891fd3508666499
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 22:37:49
Display reorder
300,125,197,138,149,114,123,195,139,147,115,148,196,124,140,116,121,193,141,145,117,122,194,142,146,118,120,192,143,144,119,203,136,131,155,112,201,137,129,153,113,202,135,130,154,111,132,199,127,151,108,133,200,128,152,109,134,198,126,150,110,301,304,303,307,273,249,272,274,275,264,250,265,267,266,271,251,269,268,270,257,248,256,258,259,261,246,260,263,262,253,247,252,255,254,240,296,297,298,299,241,289,288,291,290,242,292,293,294,295,280,243,281,283,282,284,244,285,287,286,276,245,277,279,278,319,318,320,317,209,90,9,227,226,207,91,10,223,222,225,92,208,11,224,205,93,8,218,219,206,94,6,220,221,204,95,7,216,217,88,1,215,239,238,89,0,213,234,235,87,2,214,236,237,3,84,211,230,231,4,85,212,233,232,5,86,210,228,229,312,311,313,314,185,102,26,174,161,183,103,24,175,159,176,104,184,25,160,181,105,29,177,157,182,106,27,178,158,180,107,28,179,156,100,32,191,172,167,101,30,189,173,165,99,31,190,171,166,35,96,187,168,163,33,97,188,169,164,34,98,186,170,162,305,302,308,310,75,20,44,59,61,76,18,42,57,62,58,19,77,43,60,74,23,47,55,64,72,21,45,56,65,73,22,46,54,63,15,39,81,50,67,16,40,82,48,68,17,41,83,49,66,38,14,80,53,70,36,12,78,51,71,37,13,79,52,69,306,315,316,309 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#7b2d22e166b1ff02dad840b7a1389a143f850a338adb3bda964b6fc81ff7fb8b, 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 22:37:51 · history