Equation 677 Database

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Magma 36321a907b16…

magma 36321a907b16
Size
381
Isomorphism class hash
36321a907b1670ec719665222b543df31a1789dad5c5fb6db0b94559faded5d1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:35:14
Display reorder
380,201,229,218,329,219,212,223,206,236,225,230,202,216,220,224,204,210,234,226,313,203,228,217,312,221,211,222,205,235,227,232,187,198,315,191,181,192,209,237,197,316,188,189,182,193,207,238,233,195,199,314,186,190,180,194,208,239,200,231,196,185,183,215,213,214,184,352,353,333,365,375,354,355,335,330,334,137,165,154,307,158,179,159,142,139,164,166,135,155,156,160,143,177,140,162,308,136,167,153,306,157,178,161,141,138,163,168,120,134,310,124,145,128,176,173,130,311,121,125,146,126,174,171,169,131,132,309,122,123,144,127,175,172,133,170,129,149,147,151,152,150,148,349,372,379,373,374,351,364,350,363,348,284,280,257,325,261,242,268,294,290,273,281,282,255,262,269,295,244,288,274,323,283,279,256,324,263,245,267,296,289,275,286,253,277,328,258,240,266,297,291,272,326,254,259,241,264,298,292,287,270,278,327,252,260,243,265,299,293,276,285,271,246,247,251,249,250,248,376,337,336,367,366,358,338,339,357,356,72,103,92,304,93,114,97,80,77,99,104,73,90,94,98,78,115,75,100,305,74,102,91,303,95,116,96,79,76,101,106,89,69,300,62,83,63,111,108,68,302,87,60,81,64,112,109,107,66,70,301,88,61,82,65,113,110,71,105,67,84,85,117,118,119,86,371,332,362,347,377,370,361,345,378,346,16,47,33,319,37,58,41,21,18,43,45,17,34,38,39,22,59,19,44,317,15,46,35,318,36,57,40,23,20,42,50,2,13,322,3,24,7,55,52,9,320,1,4,25,8,56,53,48,10,14,321,0,5,26,6,54,51,12,49,11,28,29,30,31,32,27,344,369,342,340,341,331,368,360,359,343 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#8cba5b6ed4bc0e61c162b64f27fa1e2741cfbd3f135b84f82d801e00b5a37c60, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:35:14 · history