Equation 677 Database

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Magma 00482e00e257…

magma 00482e00e257
Size
321
Isomorphism class hash
00482e00e2577acb432430957754a083ac365a290ee2dd717a9a7d7a99562968
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 22:50:05
Display reorder
300,80,15,87,111,104,78,16,102,88,112,79,17,103,89,113,14,83,107,86,110,12,81,105,84,108,13,82,106,85,109,21,75,99,93,117,22,76,100,94,118,23,77,101,95,119,74,20,98,92,116,90,72,18,96,114,73,19,97,91,115,315,316,303,302,264,121,266,267,265,268,122,269,270,271,273,120,272,274,275,124,261,260,262,263,125,253,252,254,255,123,257,256,258,259,127,288,289,291,290,128,292,293,295,294,126,297,296,299,298,285,130,284,287,286,279,276,131,277,278,280,129,281,283,282,320,319,318,317,234,61,224,225,235,236,62,237,226,227,238,60,239,222,223,64,232,233,216,217,65,228,229,218,219,63,230,231,220,221,67,247,246,207,206,68,249,248,209,208,66,251,250,205,204,245,70,244,213,212,215,241,71,240,214,243,69,242,211,210,309,310,307,308,145,3,160,135,169,146,4,170,161,136,144,5,168,159,137,2,148,172,156,134,1,149,173,157,132,0,147,171,158,133,9,151,175,166,141,10,152,176,167,142,11,150,174,165,143,154,8,178,162,140,163,155,6,179,138,153,7,177,164,139,311,312,304,301,24,36,186,187,48,25,37,49,189,188,26,38,50,191,190,39,27,51,184,185,40,28,52,180,181,41,29,53,182,183,42,30,54,198,199,43,31,55,201,200,44,32,56,203,202,33,45,57,197,196,193,34,46,58,192,35,47,59,195,194,313,314,305,306 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#b356224f433e80b1c4ac338e7aaea2066ee34f4a7233e2d09dbcc6e7070accf0, 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 22:50:06 · history