Equation 677 Database

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Magma a893c7841aa7…

magma a893c7841aa7
Size
321
Isomorphism class hash
a893c7841aa786c017fba2f67603caa0e1aab34ae150ac63de78bd149aa04056
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 22:27:16
Display reorder
300,107,177,213,123,5,105,3,178,214,124,106,4,179,215,125,103,176,0,212,122,104,174,2,210,120,102,175,1,211,121,98,168,11,204,114,96,169,9,205,115,97,170,10,206,116,171,101,7,207,117,208,172,99,8,118,173,100,6,209,119,311,303,302,307,88,291,289,288,290,89,294,295,293,292,87,298,299,296,297,84,287,286,284,285,85,279,278,277,276,86,283,282,281,280,94,255,254,252,253,95,259,258,256,257,93,263,262,261,260,267,90,266,264,265,268,271,91,270,269,275,92,274,272,273,319,318,320,317,20,201,243,242,159,18,160,202,247,246,19,161,203,251,250,23,200,158,239,236,21,198,156,230,229,22,199,157,235,234,15,192,150,162,67,16,193,151,163,68,17,194,152,164,66,195,14,153,165,70,166,196,12,154,71,197,13,155,167,69,313,314,305,309,58,189,128,225,147,59,148,190,126,226,57,149,191,127,227,54,188,146,131,224,55,186,144,129,222,56,187,145,130,223,64,180,138,134,216,65,181,139,132,217,63,182,140,133,218,183,60,141,137,219,135,184,61,142,220,185,62,143,136,221,301,312,304,308,78,29,38,240,241,79,244,27,36,245,80,248,28,37,249,81,25,238,41,237,82,26,228,39,231,83,24,232,40,233,76,35,111,44,48,77,33,112,42,49,75,34,113,43,50,31,72,110,47,51,45,32,73,108,52,30,74,109,46,53,310,316,315,306 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#34f20f8c77c0cbdeb0b8c0e60587a50e7d9ef4f1dbdd588ea7161aafd1a43efd, 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 22:27:18 · history