Equation 677 Database

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Magma 3c0d235dd26a…

magma 3c0d235dd26a
Size
321
Isomorphism class hash
3c0d235dd26a5606c520234643d1748c13ac8c17ed4cc01a989d4366726bc94d
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 22:33:21
Display reorder
300,124,189,44,170,91,125,190,42,168,92,123,43,169,90,191,188,120,47,173,94,186,121,45,171,95,187,122,46,172,93,180,39,130,176,89,181,40,131,174,87,182,41,129,175,88,38,183,126,179,85,36,184,127,177,86,37,185,128,178,84,305,303,302,308,141,291,290,289,288,142,294,295,292,293,143,299,296,297,298,287,140,286,284,285,279,138,278,277,276,283,139,282,280,281,255,254,132,252,253,258,259,133,256,257,263,262,134,260,261,267,266,135,265,264,271,270,136,269,268,275,274,137,272,273,317,320,319,318,50,246,223,213,247,48,248,224,214,249,49,222,215,250,251,245,53,226,212,244,240,51,227,210,241,242,52,225,211,243,229,221,56,204,228,230,219,54,205,231,232,220,55,206,233,217,235,59,207,234,218,237,57,208,236,216,239,58,209,238,313,314,312,311,15,69,201,165,155,16,70,202,166,153,17,203,167,154,71,68,14,200,164,151,66,12,198,162,152,67,13,199,163,150,60,192,21,156,146,61,193,22,157,144,62,194,23,158,145,195,63,20,159,149,196,64,18,160,147,197,65,19,161,148,306,310,304,301,4,109,29,104,80,5,110,27,102,78,3,28,103,79,108,112,1,25,107,83,113,0,26,105,81,111,2,24,106,82,115,35,10,99,75,116,33,11,100,76,114,34,9,101,77,31,118,6,98,74,32,119,7,96,72,30,117,8,97,73,316,309,307,315 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#5e8db79a467cc4283015956475779111852195ee797ae26ed1a0610c426b851f, 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 22:33:22 · history