Equation 677 Database

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Magma 211acc6d367d…

magma 211acc6d367d
Size
321
Isomorphism class hash
211acc6d367dbf2e6b8c8e9c3ff885a9e639797de8644a993735af049326c486
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 22:59:44
Display reorder
300,23,144,84,34,124,21,145,125,85,35,22,143,123,83,36,19,146,126,210,208,20,147,127,87,240,238,229,226,86,37,122,28,89,142,38,120,26,90,140,39,121,27,88,141,40,25,119,91,138,41,207,214,92,139,42,24,245,244,228,219,312,302,307,310,283,281,196,282,280,287,285,284,197,286,279,276,277,198,278,295,292,293,199,294,299,297,296,200,298,291,288,289,201,290,272,275,194,273,274,265,267,195,264,266,269,271,193,268,270,259,257,190,256,258,263,261,191,260,262,255,253,192,252,254,320,318,317,319,101,48,64,103,234,224,241,249,62,104,102,47,184,63,212,211,50,186,67,105,99,51,188,65,106,100,49,185,66,107,29,93,70,46,108,30,94,68,44,109,31,95,69,45,110,96,32,72,209,213,97,33,71,43,111,98,239,242,220,225,304,316,301,314,82,152,18,114,133,80,153,134,16,115,81,151,132,17,113,78,155,136,14,117,79,156,137,15,118,77,154,135,13,116,131,75,0,216,189,215,73,204,149,218,130,74,1,150,187,76,129,12,246,233,243,227,237,230,248,223,128,11,148,112,313,308,309,311,161,57,7,166,179,162,58,180,5,164,163,56,178,6,165,160,60,182,3,169,158,61,183,4,167,159,59,181,2,168,177,202,10,55,171,175,203,9,53,170,176,235,206,54,217,157,174,205,221,247,251,232,236,222,231,250,173,8,52,172,305,306,303,315 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#e2a478bba1a9cde7c476f091d01301457f542f6a1b857d9784efc8df77c998e9, 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 22:59:45 · history