Equation 677 Database

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Magma bdb2194d6413…

magma bdb2194d6413
Size
321
Isomorphism class hash
bdb2194d6413ee3d09be211717d6c642bf7203cd5aede3484004ed00fddf4f5a
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 22:49:14
Display reorder
300,143,162,38,73,184,144,163,71,39,76,145,164,72,37,180,165,146,75,205,231,203,147,74,35,248,246,224,212,36,189,160,179,32,141,77,161,183,33,142,78,159,70,31,140,79,188,157,34,138,80,232,228,195,139,81,158,247,238,223,213,301,312,315,314,278,276,19,277,279,282,280,281,20,283,286,285,284,21,287,289,290,288,18,291,293,294,292,16,295,297,298,296,17,299,268,269,10,270,271,272,273,11,274,275,265,264,12,266,267,252,253,13,254,255,256,257,14,258,259,261,260,15,262,263,318,319,317,320,103,199,4,196,220,219,242,239,5,115,104,88,47,3,221,214,105,45,1,116,89,106,46,0,117,90,107,44,2,118,86,51,7,101,42,87,49,8,102,40,85,50,9,100,41,48,82,6,217,207,197,83,193,99,43,84,240,236,218,206,308,306,309,304,54,151,25,132,166,52,152,133,26,167,53,153,134,27,168,154,57,135,28,169,155,55,136,29,170,156,56,137,30,171,150,130,22,208,186,227,131,204,58,229,149,129,23,59,182,202,148,194,241,234,245,225,237,209,250,226,128,24,198,191,311,303,316,313,60,109,175,122,93,61,110,123,176,94,62,111,124,177,95,112,63,125,174,96,113,64,126,172,97,114,65,127,173,98,181,120,187,66,91,185,121,178,67,92,108,222,230,68,216,201,190,235,210,243,244,233,251,211,215,249,119,192,69,200,310,302,305,307 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#a6f8f14c2d1a7a50e2f04288a5c27cfc248015f3a737479d1ca25990a259c6e6, 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 22:49:14 · history