Equation 677 Database

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Magma 65acd422b878…

magma 65acd422b878
Size
321
Isomorphism class hash
65acd422b8786d784e26ded17e010f5ee3a211f82b6f0d040a673bca3f2901f2
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 22:20:44
Display reorder
300,61,217,114,134,89,59,90,218,115,135,60,91,219,113,136,64,216,92,117,133,62,214,93,118,131,63,215,94,116,132,120,56,95,208,125,121,57,96,209,126,119,58,97,210,127,55,123,98,211,128,53,124,99,212,129,54,122,100,213,130,311,302,303,301,10,289,291,290,288,11,292,293,295,294,9,297,296,299,298,6,284,285,287,286,7,277,276,279,278,8,280,281,283,282,255,0,252,253,254,259,2,256,257,258,263,1,261,260,262,4,267,264,265,266,5,271,268,269,270,3,275,273,272,274,318,317,320,319,109,158,34,205,193,107,194,244,247,206,108,195,250,249,207,112,155,192,24,204,110,156,190,25,202,111,157,191,26,203,40,104,184,150,196,38,105,185,151,197,39,106,186,149,198,103,36,187,153,199,101,37,188,154,200,102,35,189,152,201,313,314,305,308,72,221,146,181,241,73,242,222,147,182,71,243,220,148,183,75,224,240,145,180,76,225,238,143,178,74,223,239,144,179,137,70,232,227,172,138,68,233,228,173,139,69,234,226,174,66,140,235,230,175,67,141,236,231,176,65,142,237,229,177,309,304,307,312,80,27,13,49,171,81,246,245,14,47,82,251,248,12,48,79,160,168,16,52,77,161,169,17,50,78,159,170,15,51,19,86,163,33,44,20,87,164,31,45,18,88,162,32,46,85,22,166,29,43,83,23,167,30,41,84,21,165,28,42,316,306,310,315 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#003b1571ae5bf3b67323fc5b960381c29f1c759a7de9437dd38ba69e115a500f, 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 22:20:45 · history