Equation 677 Database

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Magma 890bb423d286…

magma 890bb423d286
Size
321
Isomorphism class hash
890bb423d286e2f569477578eff906b4b1c83be6bb3388dbdb858a66f22a708b
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 22:22:52
Display reorder
300,132,202,184,208,32,133,203,185,209,30,134,201,183,207,31,198,135,180,204,35,199,136,181,205,33,200,137,182,206,34,138,193,190,214,27,139,194,191,215,28,140,192,189,213,29,196,141,186,210,26,197,142,187,211,24,195,143,188,212,25,316,315,304,306,0,268,269,271,270,2,272,273,275,274,1,264,265,267,266,252,4,253,255,254,256,5,257,259,258,260,3,261,263,262,7,293,292,294,295,8,296,297,298,299,6,289,288,291,290,277,10,276,278,279,281,11,280,282,283,284,9,285,286,287,320,319,317,318,38,236,237,66,224,36,238,239,67,222,37,234,235,68,223,228,41,229,69,227,230,39,231,70,225,232,40,233,71,226,44,249,248,64,219,42,251,250,65,220,43,247,246,63,221,241,47,240,60,218,243,45,242,61,216,245,46,244,62,217,309,310,308,307,58,151,72,158,18,59,152,73,156,19,57,150,74,157,20,154,54,75,161,21,155,55,76,159,22,153,56,77,160,23,49,149,78,164,16,50,147,79,162,17,48,148,80,163,15,145,52,81,167,12,146,53,82,165,13,144,51,83,166,14,311,312,301,303,168,91,108,103,122,169,92,109,104,120,170,90,110,102,121,94,171,111,106,125,95,172,112,107,123,93,173,113,105,124,174,89,114,101,128,175,87,115,99,126,176,88,116,100,127,85,177,117,97,131,86,178,118,98,129,84,179,119,96,130,314,313,305,302 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#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, 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 22:22:53 · history