Equation 677 Database

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Magma cd5a90b347a8…

magma cd5a90b347a8
Size
321
Isomorphism class hash
cd5a90b347a888a6aca5071598166b5d87192f82d659b1c7388cb71695dde71d
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 22:21:46
Display reorder
300,47,159,138,86,168,45,157,136,84,166,46,158,137,85,167,187,141,186,217,230,139,44,160,83,247,246,211,216,169,140,133,154,80,39,163,134,155,78,40,164,135,156,79,41,165,153,132,82,42,162,228,227,81,43,161,152,243,241,212,229,315,313,311,306,285,287,284,190,286,276,279,277,191,278,280,283,281,192,282,296,297,299,193,298,289,288,291,194,290,295,292,195,294,293,264,267,196,265,266,268,271,197,269,270,272,275,198,273,274,263,260,199,261,262,255,252,200,253,254,259,257,201,256,258,320,318,317,319,92,24,148,53,210,220,236,245,54,35,91,23,147,55,209,221,151,20,56,38,149,93,21,57,36,22,94,58,37,150,144,15,51,88,32,145,16,52,89,33,146,14,50,90,34,18,143,48,219,208,19,142,49,87,31,17,244,238,218,207,301,316,302,309,183,28,128,63,175,181,29,126,64,173,182,30,127,65,174,189,131,27,66,188,129,184,25,67,176,26,185,68,177,130,124,2,62,234,171,226,1,213,179,232,125,3,61,180,172,0,123,59,249,231,237,225,239,233,248,206,122,60,178,170,312,310,314,305,8,107,118,69,98,9,105,116,70,99,10,106,117,71,100,11,121,110,72,101,119,12,108,73,102,109,13,74,103,120,113,202,75,6,96,114,203,76,7,97,115,235,214,5,223,104,112,215,204,242,251,224,240,205,222,250,111,77,4,95,308,303,307,304 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#15e0002a5ecb0f8e7ea13fca6591bd645ffece494b3bd71abe8f3bbcdb21ed68, 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 22:21:47 · history