Equation 677 Database

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Magma 7b952ed57b21…

magma 7b952ed57b21
Size
321
Isomorphism class hash
7b952ed57b21f69d5e91b2de0450714751d839f5b3cbdeb8300deb03c41001ac
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 23:03:50
Display reorder
300,22,210,142,110,154,23,211,143,108,155,21,212,141,109,153,213,18,138,113,150,214,139,111,151,19,215,20,140,112,152,13,133,208,116,145,14,134,209,114,146,12,132,207,115,144,136,16,204,119,148,117,137,17,205,149,135,15,206,118,147,307,305,312,308,251,261,263,262,260,249,252,254,253,255,250,256,258,257,259,273,247,274,272,275,265,266,264,267,248,269,246,270,268,271,242,286,285,284,287,240,278,276,277,279,241,282,280,281,283,298,245,296,297,299,289,290,243,288,291,294,244,292,293,295,320,319,317,318,238,239,35,56,45,235,234,33,54,46,236,237,34,55,47,231,230,31,59,44,233,32,57,42,232,228,229,30,58,43,220,26,221,51,36,216,24,217,52,37,218,25,219,53,38,29,226,227,50,39,48,27,223,222,40,28,225,224,49,41,301,302,313,314,165,127,82,101,93,166,128,83,99,94,167,126,81,100,95,130,164,78,97,92,131,79,98,90,162,129,163,80,96,91,156,73,125,107,84,157,74,123,105,85,158,72,124,106,86,76,159,121,103,87,104,77,160,122,88,75,161,120,102,89,311,303,310,306,5,71,185,170,194,3,69,183,168,192,4,70,184,169,193,67,0,181,173,197,68,182,171,195,2,66,1,180,172,196,11,191,62,176,200,9,189,60,174,198,10,190,61,175,199,187,7,65,179,203,177,188,8,63,201,186,6,64,178,202,309,316,315,304 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#f4f724834d898f30c0a6fbb58eb0b496232f556dc00d71550d6e526db5e670b8, 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 23:03:51 · history