Equation 677 Database

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Magma 837b2f1f503a…

magma 837b2f1f503a
Size
321
Isomorphism class hash
837b2f1f503a65b52b7105aabf9d57b3083fef8e8e6023663bcecd3d1f39df06
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 22:49:27
Display reorder
311,248,254,260,275,85,115,130,223,84,114,131,222,82,110,132,220,83,111,133,221,247,253,261,274,108,78,216,128,109,79,217,129,107,77,215,127,105,81,219,125,252,246,273,259,106,80,218,126,63,61,62,66,64,65,59,60,284,285,283,286,301,305,300,314,295,289,293,288,210,98,191,76,211,99,192,75,212,97,195,72,213,95,193,73,214,96,194,74,103,209,68,189,290,294,287,292,104,208,67,190,102,205,70,188,100,206,71,186,101,207,69,187,165,163,164,161,162,160,156,154,158,159,157,155,310,307,308,316,43,31,201,93,44,32,202,94,244,241,271,251,45,30,204,92,245,240,272,250,46,29,203,91,35,41,86,200,36,42,87,198,37,40,88,199,242,243,249,270,33,38,89,197,34,39,90,196,18,16,17,21,19,20,23,22,280,281,279,278,304,319,306,315,291,282,277,276,117,112,13,5,118,24,12,0,256,255,237,234,119,116,15,6,120,113,14,7,26,121,3,11,238,257,233,236,25,122,4,10,28,123,2,8,27,124,1,9,239,258,232,235,55,53,54,58,56,57,50,51,48,49,47,52,309,302,303,313,145,181,170,134,146,182,171,135,144,180,172,136,148,184,173,137,149,185,174,138,147,183,175,139,269,264,262,266,268,265,263,267,179,150,140,169,177,152,141,166,178,153,142,167,176,151,143,168,224,225,226,227,228,229,230,231,298,296,297,299,317,312,318,320 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#a9f62e2491236cd33b6e554b1a4dc1a2938062e1ffa7bd655365fbe4324c4209, 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 22:49:28 · history