Equation 677 Database

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Magma 9676d2e1c5df…

magma 9676d2e1c5df
Size
321
Isomorphism class hash
9676d2e1c5df0d2b3b76e8f964c79d11ea7147bdaa76541baa675def78acb6a5
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 22:55:43
Display reorder
300,167,93,177,29,64,168,94,178,30,65,166,92,176,28,63,169,95,179,206,216,170,96,180,26,249,247,220,232,27,66,165,91,22,175,62,163,89,23,173,60,164,90,21,174,61,88,162,24,171,58,219,230,25,172,59,87,246,238,231,215,313,315,304,311,280,283,281,192,282,284,287,285,190,286,277,279,276,191,278,293,295,292,195,294,296,299,297,193,298,289,291,288,194,290,272,275,198,273,274,265,267,196,264,266,269,271,197,268,270,259,257,201,256,258,263,261,199,260,262,255,253,200,252,254,320,317,318,319,103,113,158,67,209,221,243,245,68,38,102,112,157,69,210,222,115,160,70,37,105,116,161,71,35,104,114,159,72,36,101,111,73,156,31,99,109,74,154,32,100,110,75,155,33,107,97,76,229,207,108,98,77,153,34,106,242,240,228,208,309,316,307,306,46,8,185,19,82,47,6,186,17,83,48,7,184,18,81,45,4,188,15,85,43,5,189,16,86,44,3,187,14,84,39,11,0,234,80,211,9,204,182,218,40,10,1,183,79,2,41,13,248,217,236,212,237,233,241,205,42,12,181,78,314,303,312,310,146,148,128,51,123,144,149,126,49,124,145,147,127,50,125,142,151,131,54,122,143,152,129,52,120,141,150,130,53,121,138,202,56,134,117,136,203,55,132,118,137,235,213,133,223,20,140,214,226,244,251,227,239,225,224,250,139,57,135,119,305,302,308,301 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#d33e4a3e2f8aecd7db8c3ccbf48af948a122b54aec333d772566c797fe9ef74b, 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 22:55:44 · history