Equation 677 Database

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Magma 6bc7b6646773…

magma 6bc7b6646773
Size
321
Isomorphism class hash
6bc7b664677363e41c65469bc78a5d05fbe6c2f8e5454d944e6a89bbbf8e6154
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 22:49:31
Display reorder
300,8,165,130,177,141,6,166,131,178,142,129,7,179,143,167,164,11,126,176,140,162,127,9,174,138,163,10,128,175,139,3,121,156,168,132,4,122,157,169,133,5,120,158,170,134,124,2,159,171,135,125,1,160,172,136,123,0,161,173,137,306,305,311,313,244,290,291,289,288,245,294,295,293,292,299,243,296,297,298,286,240,287,284,285,278,279,241,277,276,282,242,283,280,281,250,255,254,253,252,251,259,258,257,256,249,263,262,260,261,267,246,266,265,264,271,247,270,269,268,275,248,274,272,273,318,320,319,317,69,152,235,113,14,70,150,237,111,12,238,71,112,13,151,155,68,232,109,17,153,229,66,110,15,154,67,230,108,16,60,216,147,119,20,61,219,148,117,18,62,220,149,118,19,222,63,146,115,23,224,64,144,116,21,227,65,145,114,22,312,302,309,315,26,94,105,83,189,24,95,106,81,190,107,25,82,191,93,90,29,104,79,188,91,102,27,80,186,92,28,103,78,187,32,96,85,74,180,30,97,86,72,181,31,98,84,73,182,99,35,88,77,183,100,33,89,75,184,101,34,87,76,185,301,307,303,314,48,42,202,234,213,49,43,203,236,214,201,50,239,215,44,45,51,198,233,212,46,199,52,228,210,47,53,200,231,211,54,193,40,217,204,55,194,41,218,205,56,192,39,221,206,196,57,36,223,207,197,58,37,225,208,195,59,38,226,209,310,308,304,316 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#aa12d1af20c50a7f712e8df2ac0f984d22557fb7db3e49cc75c20296525d3597, 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 22:49:32 · history