Equation 677 Database

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Magma 7a7b01105281…

magma 7a7b01105281
Size
321
Isomorphism class hash
7a7b01105281d4414c3e932739f5e492df54b3d5f02232ab51ea263da1b373a4
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 22:32:39
Display reorder
300,158,174,114,180,70,159,71,175,115,181,173,72,160,113,179,161,170,69,110,176,162,171,67,111,177,163,172,68,112,178,165,156,61,245,246,166,157,62,249,250,1,164,155,63,185,168,152,64,108,182,169,153,65,109,183,167,154,66,107,184,315,313,307,311,269,268,270,271,13,273,14,272,274,275,265,15,264,267,266,252,253,16,254,255,256,257,17,258,259,260,261,18,263,262,293,292,19,294,295,297,296,20,299,298,291,288,289,21,290,277,276,22,278,279,281,280,23,282,283,285,284,24,286,287,319,317,318,320,89,144,83,226,126,90,127,145,84,227,143,125,88,82,225,85,140,122,79,222,86,141,123,80,223,87,142,124,81,224,150,95,117,74,232,151,96,118,75,233,73,149,94,116,231,146,91,120,77,228,147,92,121,78,229,148,93,119,76,230,304,310,306,301,239,132,190,101,52,237,53,133,191,102,131,54,238,189,100,235,128,51,186,97,236,129,49,187,98,234,130,50,188,99,138,247,58,196,244,139,251,59,197,248,195,137,243,60,106,134,241,57,192,103,135,242,55,193,104,136,240,56,194,105,308,314,303,316,203,214,41,30,10,201,11,215,42,28,213,12,202,40,29,199,210,9,37,26,200,211,7,38,27,198,212,8,39,25,220,209,0,47,36,221,207,2,48,34,46,219,208,3,35,216,205,4,43,32,217,206,5,44,33,218,204,6,45,31,312,305,309,302 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#58666f8071d01f531e6f0c3147dedbb33da52b01b6615c3c73eb980e964d7179, 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 22:32:40 · history