Equation 677 Database

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Magma eaf260678f19…

magma eaf260678f19
Size
321
Isomorphism class hash
eaf260678f19a7177a8465e5ab2f59ba43873f8977550da785cf40842e053df3
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 23:03:54
Display reorder
300,218,217,216,220,221,219,223,224,222,226,227,225,233,231,232,229,230,228,239,237,238,235,236,234,246,247,248,249,250,251,244,245,243,240,241,242,208,209,207,204,205,206,214,215,213,210,211,212,197,195,196,193,194,192,203,201,202,199,200,198,308,307,316,315,253,252,254,255,256,257,258,259,260,261,262,263,266,264,265,269,267,268,272,270,271,275,273,274,277,278,276,280,281,279,283,284,282,286,287,285,289,290,288,292,293,291,295,296,294,298,299,297,18,19,20,21,22,23,16,17,15,12,13,14,318,317,319,320,116,115,114,118,119,117,113,111,112,109,110,108,25,26,24,28,29,27,31,32,30,34,35,33,88,89,87,84,85,86,94,95,93,90,91,92,101,99,100,97,98,96,107,105,106,103,104,102,131,129,130,127,128,126,122,120,121,125,123,124,311,306,310,314,74,73,72,76,77,75,79,80,78,82,83,81,37,38,36,40,41,39,43,44,42,46,47,45,58,59,57,54,55,56,49,50,48,52,53,51,71,69,70,67,68,66,62,60,61,65,63,64,136,137,135,132,133,134,142,143,141,138,139,140,301,304,303,313,158,157,156,160,161,159,163,164,162,166,167,165,173,171,172,169,170,168,179,177,178,175,176,174,186,187,188,189,190,191,184,185,183,180,181,182,155,153,154,151,152,150,146,144,145,149,147,148,4,5,3,1,0,2,10,11,9,6,7,8,302,305,309,312 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, 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 23:03:55 · history