Equation 677 Database

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Magma 0b12aa326818…

magma 0b12aa326818
Size
321
Isomorphism class hash
0b12aa3268186426756cd188365a3e50a80796ad160e2fa1a59ce0f5a397f884
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 22:33:25
Display reorder
300,139,28,148,19,108,140,109,29,149,20,138,110,27,147,18,24,142,111,144,22,25,143,112,145,23,26,141,113,146,21,154,34,137,114,17,35,135,115,155,15,33,136,116,153,16,133,30,117,150,13,134,31,118,151,14,132,32,119,152,12,315,316,301,302,268,51,270,271,269,272,273,52,274,275,265,264,53,266,267,50,253,252,254,255,48,257,256,258,259,49,261,260,262,263,295,57,293,292,294,58,297,296,299,298,59,288,289,290,291,277,56,276,279,278,281,54,280,283,282,285,55,284,287,286,319,320,317,318,236,45,214,215,237,239,238,46,210,211,234,235,47,212,213,44,229,228,207,206,42,231,230,209,208,43,233,232,205,204,226,36,249,248,227,37,251,250,223,222,38,246,247,225,224,240,39,241,219,218,243,40,242,220,221,245,41,244,217,216,309,310,308,307,173,64,189,188,172,168,169,65,191,190,170,171,63,186,187,60,178,179,181,180,61,174,175,183,182,62,176,177,185,184,200,70,162,163,201,71,164,165,202,203,69,166,167,198,199,160,66,161,192,193,156,67,157,194,195,158,68,159,196,197,311,312,305,306,85,4,97,73,126,86,127,5,98,74,84,128,3,96,72,1,88,129,100,76,0,89,130,101,77,2,87,131,99,75,103,10,91,124,79,11,92,125,104,80,9,90,123,102,78,94,6,120,106,82,95,7,121,107,83,93,8,122,105,81,314,313,303,304 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#6086f0079822f3fde2aa4f203419cd6117656c7d05938f081a69b332c89c02c3, 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 22:33:26 · history