Equation 677 Database

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Magma aff5f4c48432…

magma aff5f4c48432
Size
321
Isomorphism class hash
aff5f4c48432e30ecfcc305e5ec27698859667064bd52125794a03766c675fe9
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 23:00:00
Display reorder
313,246,256,275,233,76,120,17,223,75,121,16,222,73,119,220,15,74,118,221,14,245,255,232,274,69,113,216,21,114,70,22,217,115,68,20,215,116,72,219,18,254,244,234,273,71,117,19,218,12,13,11,8,9,10,7,6,289,277,278,276,301,300,303,318,292,294,284,279,136,205,23,67,137,206,24,66,138,209,63,25,139,207,64,26,140,208,27,65,135,211,59,28,295,291,280,283,210,134,29,58,214,131,61,30,212,132,31,62,133,213,32,60,194,195,193,197,198,196,200,201,202,203,204,199,310,306,308,317,191,55,127,176,192,54,177,128,272,242,269,258,190,57,130,175,271,243,259,268,189,56,174,129,184,51,126,169,52,185,170,124,53,186,171,125,241,270,257,267,49,187,172,123,188,50,173,122,79,77,78,82,80,81,84,83,287,288,286,285,305,319,302,316,281,293,290,282,37,165,45,105,38,166,46,106,237,266,251,240,39,167,107,47,40,168,48,108,36,164,109,44,265,236,239,252,163,35,43,110,161,33,111,41,162,34,42,112,235,264,238,253,5,3,4,0,2,1,182,183,180,178,179,181,304,307,309,315,155,98,150,92,156,99,93,148,157,100,94,149,158,97,146,91,159,95,147,89,160,96,90,145,262,249,261,247,250,263,248,260,104,154,85,141,103,151,144,86,101,152,87,142,153,102,88,143,224,225,226,227,228,229,230,231,298,296,297,299,311,314,312,320 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#e9460cea3e471d03fe1a4dfa5e68e64aa509c8601c2a885c863435b22f6faffe, 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 23:00:01 · history