Equation 677 Database

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Magma 4cddfee1bc2d…

magma 4cddfee1bc2d
Size
321
Isomorphism class hash
4cddfee1bc2d8a1e4255ab41be6614e47b9417e84dbc61f7a54869b840811099
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 22:45:53
Display reorder
300,17,43,158,53,65,15,63,44,159,51,16,64,42,157,52,13,46,61,154,49,14,47,62,155,50,12,45,60,156,48,23,41,56,240,241,21,39,54,244,245,22,40,55,248,249,37,19,59,237,236,38,20,57,153,151,36,18,58,150,152,315,313,302,308,5,265,266,267,264,3,269,268,270,271,4,273,272,274,275,0,260,261,262,263,2,252,253,254,255,1,256,257,258,259,11,289,288,291,290,9,292,293,295,294,10,296,297,299,298,284,7,285,286,287,276,8,277,278,279,280,6,281,282,283,319,318,317,320,171,178,141,187,119,169,117,179,142,188,170,118,180,143,189,167,181,115,140,186,168,182,116,138,184,166,183,114,139,185,162,176,125,147,193,160,177,123,148,194,161,175,124,149,195,172,165,121,146,192,173,163,122,144,190,174,164,120,145,191,307,311,309,310,77,129,226,215,230,75,228,130,227,213,76,229,131,225,214,73,128,233,222,211,74,126,231,223,212,72,127,232,224,210,68,135,243,217,242,66,136,247,218,246,67,137,251,216,250,134,71,239,220,238,132,69,234,221,208,133,70,235,219,209,303,316,305,314,81,29,105,97,202,82,203,27,106,98,83,204,28,107,96,80,25,205,104,100,78,26,206,102,101,79,24,207,103,99,87,35,200,111,95,88,33,201,112,93,89,34,199,113,94,31,86,196,110,91,32,84,197,108,92,30,85,198,109,90,304,301,312,306 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#9dc1b7560e7dd8c4d9175d590a741d2999f3578c3e161e058f60df88b07e0ac9, 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 22:45:54 · history