Equation 677 Database

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Magma 1a18a627cbcf…

magma 1a18a627cbcf
Size
321
Isomorphism class hash
1a18a627cbcfef8ae49260308f9cf2314fb0eac1a14de6e720c2eeafd9a2aa61
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 22:32:11
Display reorder
300,26,151,157,118,103,27,158,119,153,101,28,155,159,120,102,150,29,160,117,100,148,30,161,115,229,234,31,162,116,99,163,142,110,24,109,164,143,111,25,107,165,144,112,23,108,145,166,113,20,105,146,167,114,21,106,147,235,230,22,104,304,302,309,314,246,290,291,289,288,247,294,293,295,292,248,299,298,297,296,286,249,287,285,284,278,250,279,277,276,282,251,283,281,280,254,255,253,244,252,258,259,257,245,256,262,263,261,243,260,267,266,264,240,265,271,270,268,241,269,275,274,272,242,273,318,320,317,319,8,189,32,140,169,9,225,233,190,170,10,191,33,141,168,188,11,34,139,172,186,12,35,137,173,187,13,36,138,171,37,180,132,14,175,38,181,133,15,176,39,182,134,16,174,183,40,135,17,178,184,41,136,18,179,185,224,232,19,177,303,301,313,307,60,201,152,211,96,61,154,212,202,97,59,200,156,213,98,197,63,149,210,95,198,64,2,208,93,199,62,1,209,94,6,193,203,58,88,7,194,204,56,89,5,192,205,57,90,196,0,206,226,91,236,3,237,55,228,195,4,207,54,92,310,305,312,316,219,78,129,43,69,217,130,44,76,70,218,77,131,42,68,81,215,128,46,65,79,216,126,47,66,80,214,127,45,67,121,84,49,223,74,122,82,50,221,75,123,83,48,222,73,87,124,52,239,71,85,231,53,238,227,86,125,51,220,72,306,315,308,311 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#520f0c8ba72cb86fc7f95b2cd25444b775e13567ed9a2b839438811596de084e, 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 22:32:12 · history