Equation 677 Database

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Magma 7533ca45c522…

magma 7533ca45c522
Size
321
Isomorphism class hash
7533ca45c522b9938d29e5b42c72a09566efcc0580c6a44560e1e96bcfa62f69
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 22:22:26
Display reorder
300,177,179,178,175,176,174,170,168,169,173,171,172,126,127,128,129,130,131,124,125,123,120,121,122,297,298,299,296,294,295,288,289,290,291,292,293,12,13,14,15,16,17,18,19,20,21,22,23,244,245,243,240,241,242,250,251,249,246,247,248,301,305,316,312,84,86,85,89,87,88,92,90,91,95,93,94,59,57,58,55,56,54,50,48,49,53,51,52,70,71,69,66,67,68,61,62,60,64,65,63,83,81,82,79,80,78,74,72,73,77,75,76,47,45,46,43,44,42,38,36,37,41,39,40,317,318,320,319,143,142,141,138,139,140,133,134,132,136,137,135,203,201,202,199,200,198,194,192,193,197,195,196,258,259,260,261,262,263,256,257,255,252,253,254,206,204,205,209,207,208,212,210,211,215,213,214,191,189,190,187,188,186,182,180,181,185,183,184,304,308,315,311,268,267,269,266,264,265,273,274,275,272,270,271,154,155,153,150,151,152,145,146,144,148,149,147,224,222,223,227,225,226,219,220,221,218,216,217,103,104,102,106,107,105,101,99,100,97,98,96,31,32,30,34,35,33,29,27,28,25,26,24,303,307,313,310,233,232,231,228,229,230,238,239,237,234,235,236,278,276,277,281,279,280,284,282,283,287,285,286,10,11,9,6,7,8,0,2,1,4,5,3,157,158,156,160,161,159,163,164,162,166,167,165,114,115,116,117,118,119,112,113,111,108,109,110,302,306,314,309 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {61} 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 22:22:27 · history