Equation 677 Database

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Magma ba46f6e880b2…

magma ba46f6e880b2
Size
321
Isomorphism class hash
ba46f6e880b2a0a6ea3066f49dc72c862f30df84abddc4191a6c943a99433b5e
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 22:50:16
Display reorder
300,44,234,232,10,25,236,45,11,26,238,228,46,230,9,24,43,47,82,6,28,83,48,36,7,29,225,49,226,8,27,80,38,0,50,31,81,39,2,51,32,79,37,1,52,30,41,76,4,53,34,42,77,5,54,35,55,40,78,3,33,303,306,315,313,241,295,294,293,292,299,242,297,296,298,291,240,290,289,288,278,244,279,277,276,283,245,282,281,280,286,243,287,285,284,258,259,256,247,257,263,262,260,248,261,255,254,252,246,253,270,271,268,250,269,275,274,272,251,273,249,266,267,264,265,317,319,318,320,88,203,178,184,65,179,89,185,66,201,177,87,202,183,67,174,84,199,180,64,200,85,175,181,62,176,86,198,182,63,194,169,190,94,56,192,170,191,95,57,193,168,189,93,58,172,197,186,90,59,173,195,187,91,60,92,171,196,188,61,302,301,309,305,16,233,115,214,235,116,17,215,239,237,114,15,229,213,231,118,12,74,210,222,75,13,119,211,223,117,14,224,212,227,69,113,205,22,220,70,111,206,23,221,68,112,204,21,219,109,72,208,18,216,110,73,209,19,217,20,108,71,207,218,312,314,310,316,103,134,145,125,166,146,104,123,167,132,144,102,133,124,165,148,106,137,121,162,135,107,149,122,163,147,105,136,120,164,140,151,131,101,157,138,152,129,99,158,139,150,130,100,156,154,143,127,97,160,155,141,128,98,161,96,153,142,126,159,307,308,304,311 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#b7ef46c52e3181531ee451cc516c519f12d29148a838b2a4381cb7ae279fb33d, 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 22:50:17 · history