Equation 677 Database

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Magma 97f227827ead…

magma 97f227827ead
Size
321
Isomorphism class hash
97f227827ead455927e6f89bbc8afe858e67d46321bc3bb15e48d8c3b508912d
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 22:38:03
Display reorder
300,63,133,124,158,56,64,131,122,155,54,157,132,65,123,55,136,66,120,150,52,134,67,121,152,53,135,226,229,149,51,61,128,116,45,1,62,129,114,46,3,60,130,115,47,2,127,57,119,48,50,125,58,117,49,0,126,59,118,224,225,312,315,304,310,246,299,297,296,298,247,291,288,289,290,293,295,248,292,294,283,249,281,280,282,287,250,285,284,286,279,251,276,277,278,244,263,261,262,260,245,255,253,254,252,243,259,257,258,256,275,240,273,274,272,267,241,265,266,264,271,242,269,270,268,317,320,318,319,147,17,84,172,235,230,15,82,173,190,171,16,146,83,191,20,143,80,175,188,18,144,81,176,189,19,145,79,174,187,138,12,90,178,184,139,13,88,179,182,137,14,89,177,183,11,141,86,180,186,9,142,87,181,185,10,140,85,233,234,302,303,306,308,42,74,193,213,170,43,75,194,211,168,212,73,44,192,169,77,41,196,209,166,78,39,197,210,167,76,40,195,208,165,33,72,199,205,162,34,70,200,203,160,35,71,198,204,161,69,36,202,237,164,227,37,236,206,232,68,38,201,207,163,316,313,301,307,26,218,93,103,159,24,219,91,104,154,102,217,25,92,156,214,22,96,106,151,215,23,94,107,153,216,21,95,105,148,32,222,99,109,7,30,223,97,110,5,31,221,98,108,6,220,28,101,112,231,239,29,228,113,8,238,27,100,111,4,309,311,314,305 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#7d1a9ea30af90bcd4d08abf0386c83ad32096e29a3d77362c99ba04d722859db, 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 22:38:04 · history