Equation 677 Database

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Magma 68f46e2c4183…

magma 68f46e2c4183
Size
321
Isomorphism class hash
68f46e2c41831365306bcbb4fa75668df2d85f23d95f0f8358480aa2c3ab99d6
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 22:55:50
Display reorder
300,80,171,157,229,243,78,172,158,230,244,79,173,156,228,245,83,170,160,232,242,81,168,161,233,240,82,169,159,231,241,75,163,177,235,249,76,164,178,236,250,77,162,179,234,251,166,74,176,238,248,167,72,174,239,246,165,73,175,237,247,315,311,304,306,61,265,264,267,266,62,268,269,271,270,60,272,273,275,274,64,260,261,263,262,65,252,253,255,254,63,256,257,259,258,67,288,289,290,291,68,292,293,294,295,66,296,297,298,299,284,70,285,287,286,276,71,277,279,278,280,69,281,283,282,319,317,320,318,94,96,225,203,208,95,97,226,201,209,93,98,227,202,207,90,99,224,199,204,91,100,222,200,205,92,101,223,198,206,85,216,102,194,214,86,217,103,192,215,84,218,104,193,213,219,88,105,197,210,220,89,106,195,211,221,87,107,196,212,307,314,316,303,13,187,45,116,123,14,188,46,114,124,12,186,47,115,125,16,190,44,119,122,17,191,42,117,120,15,189,43,118,121,19,36,185,111,129,20,37,183,112,130,18,38,184,113,131,39,22,181,110,128,40,23,182,108,126,41,21,180,109,127,305,313,302,310,7,59,144,24,139,8,57,145,25,140,6,58,146,26,138,10,55,147,27,142,11,56,148,28,143,9,54,149,29,141,5,150,50,30,137,3,151,48,31,135,4,152,49,32,136,153,0,53,33,133,154,2,51,34,134,155,1,52,35,132,301,312,309,308 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#d3adc358e0fc62ec693454af0a9d8486ee65796d63279744faf9965dafec0a65, 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 22:55:51 · history