Equation 677 Database

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Magma 0b5eea18bdfe…

magma 0b5eea18bdfe
Size
321
Isomorphism class hash
0b5eea18bdfebadc80943d121c31dc918b7386fa409a2e889dc8f8caa9489d60
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 22:54:56
Display reorder
300,71,201,3,122,53,72,51,198,2,123,199,52,73,1,121,70,194,55,6,125,196,68,54,4,126,69,236,227,5,124,77,189,48,19,128,78,190,49,20,129,21,79,188,50,127,192,76,47,18,130,193,74,45,0,131,191,75,46,225,231,305,301,306,314,248,299,297,296,298,246,290,291,289,288,295,294,247,293,292,251,283,282,281,280,287,249,286,284,285,250,279,278,277,276,243,263,262,261,260,244,255,254,253,252,257,245,259,258,256,275,242,274,273,272,267,240,266,265,264,271,241,270,269,268,318,317,319,320,44,143,158,7,232,226,153,141,159,8,142,154,43,160,9,40,139,151,157,10,140,41,152,155,11,42,138,150,156,12,35,134,146,163,13,36,132,144,164,14,165,34,133,145,15,137,38,149,162,16,135,39,147,161,17,136,37,148,233,224,302,307,311,309,29,213,90,184,176,30,174,211,88,182,212,175,28,89,183,32,209,172,86,187,210,33,173,87,185,31,208,171,85,186,27,205,168,82,179,25,203,166,80,180,81,26,204,167,181,207,23,170,228,178,237,24,234,83,235,206,22,169,84,177,304,303,313,316,57,218,202,108,120,58,118,219,197,109,217,119,56,200,107,60,214,116,91,104,215,61,117,195,105,59,216,115,92,106,63,222,112,94,100,64,223,110,95,101,93,62,221,111,99,220,66,114,97,229,239,67,230,98,103,238,65,113,96,102,310,315,308,312 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#c683f2f4b9bca41895c10e0d2ae80f929e5396dd75ded79bce8025bcd75f3dbe, 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 22:54:57 · history