Equation 677 Database

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Magma e18a24459578…

magma e18a24459578
Size
321
Isomorphism class hash
e18a2445957843d05d66e33a4b42326e5c8470bca5b30b24363a481a8eb0acaa
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 22:51:24
Display reorder
300,189,170,64,237,117,65,190,238,118,168,63,169,191,239,119,173,60,188,236,116,171,61,186,234,114,172,62,187,235,115,228,176,180,70,108,229,174,181,71,109,230,175,182,69,110,179,231,183,66,111,177,232,184,67,112,68,178,233,185,113,301,307,315,313,288,291,247,290,289,248,292,295,293,294,246,298,296,299,297,287,250,284,286,285,279,251,276,278,277,282,249,280,283,281,254,255,252,245,253,259,258,256,243,257,262,263,260,244,261,267,266,265,241,264,271,270,269,242,268,240,274,275,273,272,319,320,318,317,165,75,10,213,199,11,166,214,200,76,9,77,167,215,198,74,6,164,212,202,72,7,162,210,203,73,8,163,211,201,204,81,156,0,197,205,82,157,2,195,206,83,158,1,196,80,207,159,4,193,78,208,160,5,194,3,79,209,161,192,316,305,308,312,95,225,42,153,139,43,93,154,140,226,44,227,94,155,138,224,45,91,152,142,222,46,92,150,143,223,47,90,151,141,144,216,86,40,137,145,217,84,41,135,146,218,85,39,136,219,147,89,36,133,220,148,87,37,134,38,221,149,88,132,303,310,304,311,28,13,48,127,102,49,29,128,103,14,50,12,27,126,104,16,51,24,130,105,17,52,25,131,106,15,53,26,129,107,125,19,34,54,100,123,20,35,55,101,124,18,33,56,99,22,121,30,57,96,23,122,31,58,97,59,21,120,32,98,306,309,302,314 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#bc84586c53073a7227d3f1cff463f9e10a3c0feadba644a539b68478442af133, 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 22:51:25 · history