Equation 677 Database

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Magma 8482e29813c0…

magma 8482e29813c0
Size
321
Isomorphism class hash
8482e29813c0c044fe4a5afcf777fe2fd93c3fb8877845d3a88a157eb1f4c018
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 22:49:46
Display reorder
300,164,249,6,119,177,162,250,178,7,117,163,251,179,8,118,248,167,176,9,115,246,165,174,10,116,247,166,175,11,114,168,240,4,159,110,169,241,5,160,108,170,242,3,161,109,243,171,1,158,113,244,172,0,156,111,245,173,2,157,112,312,315,302,304,288,290,12,289,291,292,295,294,13,293,296,299,298,14,297,286,284,287,15,285,278,276,279,16,277,282,280,283,17,281,255,254,18,252,253,258,259,19,256,257,263,262,20,260,261,267,266,21,264,265,270,271,22,269,268,275,274,23,273,272,317,320,319,318,201,141,60,213,126,202,142,127,61,214,203,143,128,62,215,140,200,129,63,212,138,198,130,64,210,139,199,131,65,211,124,132,66,192,204,125,133,67,193,205,123,134,68,194,206,135,120,69,195,207,136,121,70,196,208,137,122,71,197,209,311,301,306,316,79,189,53,31,153,80,190,154,51,32,78,191,155,52,30,188,82,152,49,34,186,83,150,50,35,187,81,151,48,33,144,180,59,77,29,145,181,57,75,27,146,182,58,76,28,183,147,55,73,25,184,148,56,74,26,185,149,54,72,24,314,305,310,303,91,223,47,237,105,92,224,106,45,238,90,222,107,46,239,226,94,104,43,236,227,95,102,44,234,225,93,103,42,235,96,221,38,89,228,97,219,36,87,229,98,220,37,88,230,217,99,41,85,231,218,100,39,86,232,216,101,40,84,233,313,308,309,307 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#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, 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 22:49:46 · history