Equation 677 Database

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Magma fd1aa609e6c0…

magma fd1aa609e6c0
Size
321
Isomorphism class hash
fd1aa609e6c01f5cb4fa3589e4b471d82bf800b597af40f3df42c0581128646e
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 22:22:34
Display reorder
300,132,134,133,137,135,136,140,138,139,143,141,142,14,12,13,17,15,16,20,18,19,23,21,22,196,197,195,192,193,194,202,203,201,198,199,200,73,74,72,76,77,75,79,80,78,82,83,81,278,276,277,281,279,280,284,282,283,287,285,286,302,307,316,312,274,273,275,272,270,271,264,265,266,267,268,269,231,232,233,230,228,229,237,238,239,236,234,235,244,245,243,240,241,242,250,251,249,246,247,248,257,255,256,253,254,252,263,261,262,259,260,258,29,27,28,25,26,24,35,33,34,31,32,30,317,318,320,319,92,91,90,94,95,93,89,87,88,85,86,84,7,8,6,10,11,9,5,3,4,0,2,1,204,205,206,207,208,209,210,211,212,213,214,215,144,145,146,147,148,149,150,151,152,153,154,155,291,292,293,290,288,289,297,298,299,296,294,295,304,308,315,311,177,179,178,175,176,174,170,168,169,173,171,172,224,222,223,227,225,226,219,220,221,218,216,217,167,165,166,163,164,162,158,156,157,161,159,160,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,303,305,313,310,103,102,104,105,106,107,100,101,99,96,97,98,68,66,67,71,69,70,63,64,65,62,60,61,189,190,191,188,186,187,180,181,182,183,184,185,117,118,119,116,114,115,108,109,110,111,112,113,126,127,128,129,130,131,124,125,123,120,121,122,301,306,314,309 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {63} 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 22:22:35 · history