Equation 677 Database

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Magma 1e7a0fd76d01…

magma 1e7a0fd76d01
Size
321
Isomorphism class hash
1e7a0fd76d01df08ccce03f90621ed578545144ba060d20c3f87c1c4e272630e
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 22:37:41
Display reorder
300,83,24,115,41,125,81,25,116,39,123,82,26,114,40,124,27,79,118,37,121,28,80,119,38,122,29,78,117,36,120,74,30,113,47,131,72,31,111,45,129,73,32,112,46,130,33,77,109,43,127,34,75,110,44,128,35,76,108,42,126,315,316,302,301,272,4,273,274,275,265,5,264,266,267,269,3,268,270,271,1,256,257,258,259,0,260,261,262,263,2,252,253,254,255,296,10,297,299,298,289,11,288,291,290,293,9,292,295,294,6,280,281,283,282,7,284,285,287,286,8,277,276,279,278,320,319,318,317,238,146,239,209,208,234,144,235,205,204,236,145,237,207,206,149,230,231,215,214,147,232,233,211,210,148,228,229,213,212,251,152,250,220,221,247,150,246,216,217,249,151,248,218,219,155,243,242,226,227,153,245,244,222,223,154,241,240,224,225,309,310,308,307,142,16,96,190,191,143,17,97,187,186,141,15,98,188,189,12,138,99,182,183,13,139,100,184,185,14,140,101,180,181,133,22,102,203,202,134,23,103,198,199,132,21,104,201,200,18,136,105,195,194,19,137,106,197,196,20,135,107,193,192,311,312,305,306,70,52,91,167,166,71,53,92,162,163,69,51,90,165,164,48,66,94,158,159,49,67,95,160,161,50,68,93,157,156,61,58,89,179,178,62,59,87,174,175,60,57,88,176,177,54,64,85,171,170,55,65,86,173,172,56,63,84,168,169,313,314,303,304 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#7662547f1ab019fdebb7f412cf128566d4c1d6f1fe751ad78d224fe85422d2cf, 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 22:37:42 · history