Equation 677 Database

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Magma ecc75cd0473b…

magma ecc75cd0473b
Size
321
Isomorphism class hash
ecc75cd0473bb09daa14af8b40cfd50615d835449fc2dd48c9dff79ada5ce258
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 22:55:11
Display reorder
300,213,12,69,237,124,13,238,214,70,125,14,239,215,71,123,15,236,212,68,120,16,234,210,66,121,17,235,211,67,122,60,204,228,18,130,61,205,229,19,131,62,206,230,20,129,207,63,231,21,126,208,64,232,22,127,209,65,233,23,128,303,301,315,311,291,248,290,288,289,246,292,294,295,293,247,296,298,299,297,251,284,287,286,285,249,276,279,278,277,250,280,282,283,281,254,255,252,243,253,259,258,256,244,257,262,263,260,245,261,267,266,265,242,264,271,270,269,240,268,274,275,273,241,272,318,319,320,317,167,78,144,225,135,79,226,165,145,136,80,227,166,146,137,81,224,163,147,134,82,222,164,148,132,83,223,162,149,133,150,158,216,76,141,151,156,217,77,142,152,157,218,75,143,161,153,219,72,140,159,154,220,73,138,160,155,221,74,139,316,302,308,314,11,178,105,30,92,179,31,9,106,90,177,32,10,107,91,174,33,7,104,95,175,34,8,102,93,176,35,6,103,94,96,2,28,169,87,97,1,29,170,88,98,0,27,168,89,5,99,24,172,86,3,100,25,173,84,4,101,26,171,85,304,310,306,313,188,113,49,201,47,111,202,186,50,45,112,203,187,48,46,109,200,191,52,43,110,198,189,53,44,108,199,190,51,42,55,183,192,119,38,56,184,193,117,36,54,185,194,118,37,182,58,195,115,41,180,59,196,116,39,181,57,197,114,40,307,309,305,312 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#c8b00e8ba82c54826bf93ef2b9b2d8eeb61b8eb7ac0797b661231f1bb38e050b, 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 22:55:12 · history