Equation 677 Database

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Magma 91e7abc4ce12…

magma 91e7abc4ce12
Size
321
Isomorphism class hash
91e7abc4ce1262fd5f7011c3db21a646a56dc092ec4dee498dbfa0e075b2f2df
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 22:38:15
Display reorder
300,57,59,153,204,159,55,160,60,154,205,58,158,56,152,203,161,53,62,156,207,162,54,63,157,237,234,52,61,155,206,48,164,65,151,209,165,66,149,46,210,163,64,150,47,208,68,166,147,51,212,69,167,148,49,213,67,235,233,50,211,304,315,301,310,246,258,259,257,256,247,263,261,262,260,253,255,248,254,252,271,249,269,270,268,275,250,273,274,272,267,251,264,266,265,244,283,281,282,280,287,285,286,245,284,279,277,278,243,276,293,295,294,240,292,297,299,298,241,296,288,291,290,242,289,320,318,319,317,10,92,126,169,70,11,226,229,127,170,91,71,9,125,168,72,6,94,129,172,73,7,95,130,173,74,8,93,128,171,0,75,97,132,175,76,98,133,2,176,77,96,131,1,174,100,78,134,4,178,101,79,135,5,179,99,227,231,3,177,308,313,306,302,85,36,137,17,34,86,32,37,138,18,35,33,87,136,19,30,88,39,140,20,31,89,40,141,21,29,90,38,139,22,83,25,42,143,15,23,43,144,84,16,24,41,142,82,14,45,28,146,228,12,224,26,232,80,225,44,27,145,81,13,309,305,312,316,219,192,114,108,186,217,187,193,115,109,191,185,218,113,107,189,215,195,117,111,190,216,196,118,112,188,214,194,116,110,223,184,198,120,106,182,199,121,221,104,183,197,119,222,105,201,181,123,239,103,202,236,124,238,230,200,180,122,220,102,307,311,314,303 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#82fe73547f12a148ba897be501ddca2fd72765d56930c9a3792aacda34cfdc1d, 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 22:38:21 · history