Equation 677 Database

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Magma b6ca57a6954c…

magma b6ca57a6954c
Size
321
Isomorphism class hash
b6ca57a6954c7abdb90b7dc201297fd28aa6062cc60ec699b47fdfd6c724d1bc
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 22:49:35
Display reorder
300,84,41,56,50,75,85,39,57,51,73,86,40,55,52,74,87,37,53,49,77,88,38,54,47,228,229,223,225,48,76,34,82,61,42,70,32,83,62,43,71,81,33,60,44,72,78,36,58,45,69,79,35,59,46,68,80,222,226,224,227,304,315,316,305,152,285,287,284,286,153,276,278,277,279,151,280,282,281,283,148,297,299,296,298,149,288,290,289,291,150,292,294,293,295,265,143,266,264,267,269,144,270,268,271,142,273,274,272,275,146,260,263,261,262,147,252,255,253,254,145,256,258,257,259,320,318,317,319,92,128,165,3,236,230,234,238,4,137,93,127,164,5,138,91,131,168,6,141,89,129,166,7,139,90,130,167,8,140,124,97,161,9,134,125,98,162,10,135,99,126,163,11,136,96,123,160,12,133,94,122,159,13,132,95,233,237,220,235,309,314,310,311,67,179,105,195,194,192,177,103,188,169,66,178,104,189,170,64,175,101,186,171,65,176,102,187,172,63,174,100,185,173,184,210,110,219,218,182,216,108,207,206,204,183,109,213,212,198,181,107,251,250,248,239,231,245,244,242,180,106,201,200,301,302,303,306,1,118,18,193,190,191,116,19,154,27,0,117,20,155,28,30,121,21,158,25,31,119,22,156,26,29,120,23,157,24,113,208,16,217,215,114,214,17,205,203,202,115,15,211,209,197,112,2,249,246,247,232,221,243,241,240,111,14,199,196,308,312,307,313 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#ad2693ca9f316a407649b357541de7a5de95f31142bb6f4854bfa44084f1f633, 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 22:49:36 · history