Equation 677 Database

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Magma 1798109721d9…

magma 1798109721d9
Size
321
Isomorphism class hash
1798109721d96934788cd50d1066e72790163e851c2bc4a62be4217a6d7fb4c2
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 22:55:04
Display reorder
300,61,70,3,16,138,2,71,14,136,59,60,72,4,15,137,73,63,168,19,140,74,62,1,17,235,226,225,238,18,139,56,68,5,11,133,12,57,69,6,134,58,67,7,13,135,64,55,8,10,132,65,54,9,0,131,66,224,220,221,234,315,305,312,302,286,34,287,284,285,279,35,277,276,278,282,36,283,281,280,33,298,299,296,297,31,290,291,289,288,32,294,295,293,292,266,40,267,264,265,268,270,41,271,269,274,42,275,272,273,39,262,263,261,260,37,254,255,253,252,38,258,259,257,256,320,318,317,319,46,21,105,119,228,230,222,233,85,47,48,20,104,120,86,23,45,101,118,89,24,43,102,116,87,22,44,103,117,88,51,26,109,111,82,112,52,27,110,83,53,25,108,113,84,29,50,106,114,81,30,49,107,115,80,28,223,231,232,227,307,303,308,301,149,129,177,195,194,178,192,188,172,150,151,130,179,189,173,128,148,176,186,171,126,146,174,187,169,127,147,175,185,170,154,208,182,219,218,207,155,215,183,206,156,204,184,213,212,198,153,181,251,250,248,236,239,245,244,242,152,180,201,200,313,310,311,314,164,144,97,191,190,95,193,76,124,165,166,145,96,75,125,143,167,100,79,122,141,163,98,77,123,142,157,99,78,121,158,211,92,214,217,202,159,216,93,203,160,205,94,210,209,199,161,91,246,247,249,237,229,240,241,243,162,90,196,197,309,316,304,306 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#c6bb22b65ea8da42821d53c407d340f5ca33ab54805c0683c0d4385c20756f88, 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 22:55:05 · history