Equation 677 Database

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Magma 22ee0bb060a4…

magma 22ee0bb060a4
Size
321
Isomorphism class hash
22ee0bb060a4071e7c4e3eed846394c31b0e067ef5b40211cc3794190a1c9b6a
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 22:32:55
Display reorder
300,44,84,30,173,162,45,163,82,31,174,46,161,83,29,175,43,87,158,33,172,41,85,159,34,170,42,86,160,32,171,28,35,90,153,164,36,88,154,26,165,37,89,152,27,166,93,38,156,24,167,91,39,157,25,168,92,40,155,23,169,310,304,305,302,127,288,291,290,289,125,292,293,295,294,126,296,297,299,298,123,285,284,287,286,124,276,277,279,278,122,281,280,283,282,255,118,253,252,254,116,256,257,259,258,117,260,261,263,262,264,121,265,267,266,269,119,268,271,270,273,120,272,275,274,317,318,319,320,142,22,209,221,77,140,78,0,210,222,141,251,249,211,223,145,3,80,208,220,143,4,81,206,218,144,2,79,207,219,200,148,6,75,212,146,7,76,201,213,147,5,74,202,214,9,151,71,203,215,10,149,72,204,216,8,150,73,205,217,314,313,309,307,57,245,186,234,197,58,198,246,187,235,56,199,247,185,233,53,244,196,182,230,54,242,194,183,231,55,243,195,184,232,177,48,236,188,225,49,237,189,178,226,47,238,190,176,224,239,51,191,180,228,240,52,192,181,229,241,50,193,179,227,312,306,301,303,128,20,97,62,95,129,96,21,1,63,130,94,248,250,64,131,19,98,99,61,132,17,101,100,59,133,18,103,102,60,105,134,11,104,68,135,12,106,107,69,136,13,109,108,70,14,137,110,111,67,15,138,112,113,65,16,139,114,115,66,315,311,308,316 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#58f4898eb0f0372a4c749060353e7621900aa789e1d944064f9989e660cee0fd, 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 22:32:55 · history