Equation 677 Database

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Magma de3aa70b4ba3…

magma de3aa70b4ba3
Size
321
Isomorphism class hash
de3aa70b4ba3394d7fe425c23e0654209e4fe156b3176fc5d348889f89506df5
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 22:28:44
Display reorder
300,96,120,144,132,108,97,121,145,133,109,98,122,146,134,110,99,123,147,135,111,100,124,148,136,112,101,125,149,137,113,102,126,150,138,114,103,127,151,139,115,104,128,152,140,116,129,105,153,141,117,130,106,154,142,118,131,107,155,143,119,315,316,302,303,6,269,268,270,271,7,273,272,274,275,8,264,265,266,267,9,253,252,254,255,10,257,256,258,259,11,261,260,262,263,4,292,293,295,294,5,296,297,299,298,3,288,289,291,290,276,1,277,279,278,280,0,281,283,282,284,2,285,287,286,320,319,318,317,59,236,237,226,227,57,238,239,222,223,58,234,235,224,225,55,228,229,218,219,56,230,231,220,221,54,232,233,216,217,50,249,248,209,208,48,251,250,205,204,49,247,246,207,206,241,53,240,215,214,243,51,242,211,210,245,52,244,213,212,309,310,308,307,64,156,36,169,24,65,157,37,170,25,63,158,38,168,26,60,159,39,172,27,61,160,40,173,28,62,161,41,171,29,70,162,42,175,30,71,163,43,176,31,69,164,44,174,32,165,66,45,178,33,166,67,46,179,34,167,68,47,177,35,311,312,301,304,12,74,84,189,188,13,72,85,191,190,14,73,86,187,186,15,77,87,180,181,16,75,88,182,183,17,76,89,184,185,18,80,90,201,200,19,78,91,203,202,20,79,92,198,199,83,21,93,193,192,81,22,94,195,194,82,23,95,197,196,313,314,305,306 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#49acd73e7fb20809c4c5aee6104079a0019ec0e0539c0b91c35b8b4466bd197d, 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 22:28:45 · history